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PEEFACE. 



6r 



Little more will be expected from a work of the 
following description^ than that it should contain an 
intelligible and concise exposition of those facts and 
principles which form^ as it were^ the groundwork of 
logical science. Necessarily^ therefore^ it must be, for 
the most part, a compilation of such views as have 
obtained general acceptance, and can lay but little 
claim to any high degree of originality. 

At the same time, I may be permitted to state that 
some features exist which serve to distinguish this 
Treatise from its numerous predecessors, and which 
will, I hope, prove of service to the student by inciting 
him to examine for himself such theories and principles 
as come under his notice. Those features to which I 
more particularly allude, are the reference of all so- 
called ^^ Immediate Inferences ^^ to the class of syllo- 
gisms j the grounds for an extended adoption of Aris- 
totle^ s Dictmn ; the refutation of the charge that every 
syllogism involves a petitio principii ; the explication 
of the inductive theory in Applied Logic ; and, finally, 



IV PKEFAOE. 

the doctrine of classification^, by which every detail and 
branch of Logic is shown to exist in harmonious 
unison. And as these views are^ in a measure^ opposed 
to those contained in works of great repute^ I have 
appended to the body of this Treatise four Articles, 
wherein are set forth such arguments as I think suffi- 
cient to justify me in advancing the above-mentioned 
doctrines. 

I also deem it advisable to state that it has been my 
endeavour to give this work as suggestive a character as 
possible j and^ therefore, although it belongs to a rudi- 
mentary series, professing to treat only upon the first 
elements of Logic, I am yet not without hope that it 
will be found a sufficient introduction to such compre- 
hensive and elaborate treatises as those of Mr. Mill, 
Professor De Morgan,, and others. But while I have 
thus been compelled to satisfy myself in many cases with 
an enunciation rather than with a full investigation of 
certain doctrines, I still trust that, in the following 
pages, the student will find all that is really requisite 
to give him a fair, practical knowledge of Logic. 

The chapter on Applied Logic is, I am sensible, but 
a mere sketch. As, however, to do justice to so vast a 
subject would require a great extension of the present 
limits, and would thus curtail the utility of this 
Treatise by enhancing its price, I have contented 
myself with directing the student^s attention to such 
points as are most important, both in theory and prac- 
tice. For the same reason, nothing beyond the bare 
outlines is given of such new doctrines as I have here 



TREFACE. 



adopted; all further development of them beiog de- 
ferred to a future occasion. 

I take this opportunity of acknowledging my many 
and great obligations to those writers upon Logic 
whose works I have consulted ; and although it may 
seem invidious to particularise^ yet as^ for reasons 
which will be found specified in their proper place, I 
have expressly referred to Mr. John Stuart Mill^ as 
being the advocate of certain opinions which are com.- 
bated in the following pages, I think it only just that 
I should here record my admiration for the profound 
philosophy and great attainments which are so apparent 
in the writings of that gentleman. 

S. H. E. 

London, January, 1865. 



CONTENTS. 



Page 
Introduction 1 



CHAPTER I. 

An Inquire into the Various Members oe an Argument . . 7 
» 

CHAPTER ir. 

Op Notions or Terms : — 

§ 1. Simple-apprehension 14 

2. Abstraction of Common -notions 16 

3. Predicables, Extension, and Intension 18 

4. Division of Common-notions 18 

5. Positive, Negative, and Privative Te^'ms ...... 20 

6. Definition 21 

7. Names and their Divisions 22 

8. Opposition of Terms 23 

9. Structure of Terms 24 

10. Conclusion and Recapitulation 24 

CHAPTER III. 

Of Judgments or Propositions : — 

§ 1. Formation of Judgments 27 

2. Categorical Propositions 28 

3. Hypothetical or Conditional Propositions 29 

4. Disjunctive or Alternative Propositions 29 

5. Quantity of Propositions 30 

6. Quality of Propositions 30 

7. Distribution of Terms 31 

8. Relation of Terms 32 



CONTENTS. 

Pa2'e 

9. Systematic Classification of Propositions 38 

10. Table of Possible Propositions 'SS 

1 1 . Interpretation of the Copula 34 

12. On some other Properties of Judgments 85 

13. Concluding Remarks 35 



CHAPTER IV. 

Of Reasoning or Argument — Syllogisms: — 

§ 1. Reasoning in General 38 

2. Syllogisms — Inference 39 

3. Opposition 41 

4. Conversion 44 

5. Coincident Junction 47 

6. Mediate Inference formally expressed as such — its Divisions 48 

7. The Fundamental Law of Mediate Inference 49 

8. Of Figure * 54 

9. Remarks upon the Four Figures 54 

10. Of Mood or Mode 57 

11. Table of Valid Syllogisms 58 

12. Induction and Deduction 61 

13. Extension and Intension 64 

14. Denomination . 66 

15. Syllogistic arrangement of Propositions 66 

16. Conditional Syllogisms . 67 

17: Disjunctive Syllogisms 72 

18. The Dilemma 73 

19. Incomplete Syllogisms 75 

20. Complex Arguments, or Chains of Reasoning .... 76 

21. Recapitulation 80 

22. Conclusion 82 



CHAPTER V. 

Of Fallacies: — 

§ 1. Applied Logic in genera 84 

2. Classification of Fallacies 85 

3. Formal Fallacies 88 

4. Material Fallacies — (^uarternio Terminorum 90 

5. Material Fallacies — Premiss unduly assumed 95 

6. Material Fallacies — Ignoratio Elenchi . Ill 

7. Conclusion 115 



CONTENTS. IX 

CHAPTER VI . 

Page 
Of Logic as Practically Applied : — 

§ 1. Introductory Remarks 117 

2. Observation 119 

3. Reflection — 

1^. Of Laws and Causes .......... 126 

2«. Of Induction J 31 

3°. Of Deduction, Hypothesis, and A^erilication . . . 140 

4«. Of Analogy 143 

5^. Of Chance and Probability ]45 

6°. Examples of Reflection — 

a. The Discovery of Neptune 148 

h. Kirchhoff's Researches on the Solar Spectrum . 150 

4. Conclusion 152 

/ 

APPENDIX. 

A On Judgments 155 

B. On the so-called Immediate Inferences 159 

C. On the Dictum de Omni et Nullo 163 

D. On the Syllogism considered as a Petitio Principii . . . 166 



I 



LOGIC. 



INTRODUCTION. 

Logic may be not inaptly described as the grammar of 
thought ; that is to say, it reveals and explains the principles 
according to which our judgments are formed, in much the 
same manner as grammar analyses the laws W'hich regulate 
the expression of our thoughts by means of speech. It will, 
therefore, be seen that Logic is a science of universal extent, 
inasmuch as wherever any process of reasoning is carried 
on, there will be found, in full operation, those mental laws 
which it is the office of Logic to examine and systematise. 
It does not, however, follow that every person who reasons is 
a logician, for it is only when a process of judgment is carried 
on in regular order, and according to the rules derived from 
a study of the science, that such an appellation could be 
justly bestowed. And, in Hke manner, it would be absurd to 
suppose that there can be no correct reasoning without a good 
knowledge of Logic; for, in order to perceive the error of such 
a view, we have only to consider for a moment the mode in 
which every science is formed. Take, for example, the science 
of astronomy : the heavenly bodies had been urged through 
space, by the operation of definite cosmical laws, for ages 
previous to the discovery of those laws by human philosophers, 
and it was the very fact of such motions being in progress, 
which led to the investigation of the principles concerned; 

B 



^ INTRODUCTION. 

Thus, too, with regard to Logic : men had thought and rea- 
soned according to certain laws, long before Aristotle, by ob- 
serving and reflecting upon the various judgments which 
came under his notice, was able to enunciate the great funda- 
mental truth upon which they were based. It is from con- 
siderations such as these that we speak of scientific discoveries, 
and not of scientific inventions ; for the latter term can only 
be applied to some new method of accomplishing a specific 
object, while the former is always used when we speak of any 
fresh law or principle, which, previously existing, has been 
brought to light by the exertions of the philosopher. Like, 
then, as Newton discovered gravitation, so did Aristotle dis- 
cover the syllogism ; and, therefore, the notion that the use of 
the syllogism is merely one method of reasoning, is at once 
shown to be altogether erroneous. The truth is, that there 
can be no other process of forming a judgment, since every 
conceivable example of reasoning may, by the application of 
certain rules, be reduced to the syllogistic form. 

From what has now been said, the true value of Logic will 
be easily discerned, and as its subject is one which lies at the 
root of all other sciences, its importance can hardly be over- 
estimated. Its principal use is that it enables us to reason 
correctly, by furnishing us with various rules and standards 
Avherewith to test the validity of any argument that may be 
brought before us. And here it is requisite to guard against 
a very prevalent misconception ; I allude to the idea, that, 
by means of Logic, one may ascertain the truth or falsehood 
of any statement. The source of this error is to be found in 
the supposition that Logic is concerned with the subject of the 
various statements (technically, propositions) whose relations 
to each other it investigates ; whereas, in reality, it merely 
considers their form. Thus, the two propositions, ** Water 
is a fluid," and, " Evil is good," would by a logician be con- 
sidered as precisely similar, although one of them is false^ 



INTRODUCTION. 3 

and the other true. Again, the following argument or 
syllogism — 

All fluids are poisonous, 

Water is a flaid ; 
Therefore Water is poisonous, 

is perfectly valid and correct, although the conclusion arrived 
at is false. To render this point quite j)lain and intelligible, 
let us adopt the following course : it w^as above stated that 
Logic merely considers the foriin and not the subject (or 
matter) of propositions ; accordingly, for all logical purposes, 
we shall not alter the nature of the propositions employed, if 
we substitute letters for the words we used to express the 
substances or notions of which we spoke. Thus, instead of 
*' water is a fluid," let us say ** A is B," and for " evil is good," 
let us put '^ is D : " we then see at once, that in both in- 
stances we use exactly the same kind of proposition. Again, 
let us similarly convert tlie syllogism : we have — 
All A's are B, 
C is an A; 
Therefore C is B; 
an argument which remains unalterable in form, no matter 
what ideas are expressed by the letters.* 

This it is which confers such rigorous accuracy upon all the 
results and developments of Logic. Indeed, as Professor De 
Morgan has said. Mathematics and Logic are the two exact 
sciences. The primary doctrines of chemistry may require 
alteration as new combinations of the elements are brought to 
light ; the progressive theories of physiology are modified with 
every advance of microscopical investigation ; the glorious 
revelations of astronomy present an ever-changing aspect ; 
but Logic, like Mathematics, abides, eternal and immutable. 

The preceding remarks will probably have pointed out to 
the reader that Logic is concerned with language as distin- 

^ For further information as to form and matter see page 39 et seq. 



4: INTRODUCTION. 

guished from the ideas conveyed by the use of words ; but 
in order that the student may be well grounded in the funda- 
mental truths of the science before he proceeds to study its 
details, I shall add some further observations upon this point. 
Language in its ordinary sense, that is, speech, is useful as 
a means of communication in two ways : it enables us to 
minutely describe, or, in other words, to analyse, our various 
ideas, and it also enables us to convey, by a single sound or 
sign, the combined impression of many particulars. Take, for 
example, this description : 

" I gazed upon her form 
Transcendent, and upon her face which gleamed 
Pale through her tears, like some fair statue bathed 
In tlie cold moonlight ; and I marked the mute, 
Sad eloquence of that love-charged heart 
Which quickly heaved its alabaster veil 
In trembling fear." 

Here gradually dawn upon us the many subjects of atten- 
tion which exist in a single object, and it is only by means of 
a protracted analysis such as the above, that we are able to 
convey a complete idea of it. But then, again, we sometimes 
w^ish to express the notion of a numerous class of objects, in 
such a manner that the impression produced may serve for 
any one of them. Thus, suppose the objects were men, 
horses, cows, sheep, lions, &c. : we should merely confine our 
attention to those points in which they resembled each other, 
and should bestow a name upon this group of qualities, such 
as '* animal," by the use of which we might attain the desired 
end. This process is the reverse of the first, but at the same 
time is in a measure dependent upon it, for in order to ascer- 
tain the points of resemblance between various objects, a partial 
analysis is at all events necessary. Accordingly, Logic takes 
cognizance of both operations, and investigates the relations 
which subsist between them and the act of reasoning itself. 



INTRODUCTION. 5 

It has been said above that language enables us to convey, 
by a single sound or sign, the combined impression of many 
particulars. Now it is our ability to do this, which alone 
enables us to conduct a process of reasoning ; or otherwise we 
should find it impossible to judge of the relations between two 
ideas or objects — a condition which is evidently essential to an 
argument. One of the most curious proofs of this is afforded 
by deaf-and-dumb persons, who, when they have once been 
taught to speak by means of their fingers, are observed to 
use this means of recording their impressions, even when 
thinking alone. And it has been asserted, that '^ it will be 
found by any one who will question a deaf-mute who has 
been taught language after having grown up, that no such 
thing as a train of reasoning had ever passed through his 
mind before he was taught."* 

We have hitherto considered Logic purely as a Science, 
but it is very frequently regarded as an Art, and perhaps it 
is this mode of viewing it which holds out the strongest in- 
centive to the student. For it can only be the few who will 
voluntarily engage in the study of principles which, complete 
in themselves, give promise of no result beyond that delight 
which naturally arises from the consideration of organic 
symmetry and perfection ; the great majority being altogether 
occupied with the hope of turning their knowledge to some 
useful purpose. Therefore, in the following pages I shall 
endeavour to give as practical an effect as possible to the 
various laws of thought which we shall investigate ; and the 
student will thus find that Logic, instead of being merely an 
" ingenious recreation,'* is in reality a powerful aid to the pro- 
secution of all other studies. Not that reasoning alone will 
suffice for the discoveri/ of truth, as to do this an extended 
observation of facts is indispensable ; but when we have col- 
lected a sufficient quantity of facts, we shall find that an 

* Whately's *' Logic," p. 13. 



D INTRODUCTION. 

acquaintance with Logic will greatly assist us in deducing a 
correct inference. 

I now trust that a tolerably clear notion has been gained 
of the nature and extent of Logic ; and in the next place I 
shall briefly describe the method of proceeding which I intend 
to adopt in my explanation of the science. First, then, it wnll 
be advisable to select some example of pure reasoning, and, 
having dissected it, to point out the various members of which 
it is composed, together with the principles which form, as it 
were, the framework of the structure. We shall thus obtain 
a bird's-eye view of the country before us, and we shall be 
able to advance without doubt or hesitation to the end of our 
journey. Accordingly, it will next become our duty to examine 
each branch separately and in detail, which being done, we 
shall proceed to the consideration of the various combinations 
formed by these branches, and so at length we shall be enabled 
to construct, or to analyse at pleasure, any train of argument, 
however extensive it may be. Here, strictly speaking, the 
study of Logic as such should terminate ; but in order that 
the utility of this treatise may be increased, I shall devote a 
chapter to the discussion of the several fallacies which are of 
most frequent occurrence, giving such rules for their treat- 
ment as have been found most effectual. The concluding por- 
tion of the work will consist of some remarks upon the proper 
application of Logic, with various illustrative examples. 

Such is the course which I propose to take, and if the 
student be not dismayed by the shadowy anticipation of tech- 
nical difficulties which have no real existence, he will find an 
ample reward for all his labours. A systematic regulation 
of his intellect ; a probe wherewith to examine the most 
mysterious doctrines of philosophy ; a wand before whose 
potent touch the stately fabric of deceit and fraud will dis- 
appear ; — these are bat a few of the benefits to be obtained by 
a study of Logical science. 



A THEATISE ON LOGIC. 



CHAPTER I. 

AN INQUIRY INTO THE VARIOUS MEMBERS OF AN ARGUMENT. 

It lias already been stated that our first step towards a right 
understanding of Logic must be a strict examination of some 
definite argument. Now, as we are not all concerned with 
the subject of the reasoning, it will be the best plan for us to 
choose some example wdiich shall present us with the fewest 
and most simple ideas, so that we may devote our whole at- 
tention to the reasoning process^ and not be led aside by any 
extraneous matters. Accordingly, let us take for the subject 
of our investigation, the proof of Euclid's first proposition, 
which may be thus stated in arguments or syllogisms. 

1. The radii of the same circle are ,.- «^- ..^ 

equal to one another, / y V 

A and A B are radii of the ^ 4 -^'3 eJ 

same circle BOD; \^ \ /' 
.•. A is equal to A B. *'*- --"- -'''* 

2. The radii of the same circle are equal to one another, 

B and A B are radii of the same circle A E ; 
.*. B is equal to A B. 

3. Things which are equal to the same thing are equal 

to one another, 
A and B are equal to the same thing (viz. A B); 
.*. A C is equal to B C. 
Taking any one of the above syllogisms, we see that it is 
composed of three statements, among which this relation sub- 
sists : that if we admit the truth of the first two, we cannot 



8 AN INQUIRY INTO THE 

avoid admitting the truth of the last. This last statement is 
termed the conclusion ; the other two being called the pre- 
mises. And here the question comes — why is it, that, having 
admitted the premises, we are compelled to admit the conclu- 
sion ? To answer this we must examine the constitution 
of each premiss, and ascertain whatever is implied thereby. 
Thus, in the first of the syllogisms given above, we find 
as a commencement, the following assertion or proposition: 
— '' radii of the same circle are equal to one another :'* 
w^here a certain property, viz., " equality," is asserted, or, 
in logical language, predicated^ of a group or class of objects, 
viz., ^* radii of the same circle." That is to say, *' equality " 
is a property common to every individual comprehended in 
the class. The second proposition is to this effect : — " A C 
and A B are radii of the same circle ;'* that is, w^e assert A C 
and AB to be individuals of that very class, concerning 
which we admitted that " equality " was common to every 
one of its members. Consequently we are compelled to 
admit that AG and A B possess the property of *^ equality," 
and this admission forms the conclusion. 

Our mode of procedure has therefore been as follows : we 
first predicate something of a certain class of objects ; we 
then assert that certain individuals belong to that class; and 
lastly, we predicate the same thing of the individuals which 
we had predicated of the class. 

Now suppose the syllogism had stood thus : ** Kadii of the 
same circle are not equal to one another ; A C and A B are 
radii of the same circle ; therefore A C is not equal to A B :" 
it would still be perfectly valid, for, having denied that a 
certain property is enjoyed by a class of objects among which 
we admit certain individuals to be, w^e must necessarily deny 
that those individuals possess the property in question. 

We thus arrive at this axiom or law : ** Whatever is affirmed 
or denied altogether of any whole, may in like manner be 
affirmed or denied of any individual part belonging to, or 
comprehended in, that whole." Aristotle was the first who 
distinctly enunciated this great truth, and it is commonly 
known as '^ Aristotle's Dictum," or the ** dictum de omni et 
mdloJ' 



VARIOUS MEMBERS OF AN ARGUMENT. » 

It may at first seem strange that a statement so simple and 
obvious should be characterised as a great truth ; but a very 
little reflection will soon convince us that any law which is of 
universal extent and application, must be the more valuable 
according as it is the more simple ; and therefore it is with 
justice that Aristotle is honoured for having enabled us to 
explain the formation and examine the validity of any argu- 
ment whatever, in so plain and satisfactory a manner. Another 
fact also which will appear improbable, is that the dictum may 
be universally applied ; that is to say, no syllogism can be 
valid or admissible unless it strictly complies with the require- 
ments of the dictum, and in a later portion of this w^ork rules 
will be found by means of which it is possible to bring every 
specimen of reasoning to this test. Indeed, if we w^ould 
become thoroughly acquainted with the principles of logical 
science, we must invariably bear in mind the dependence of 
every train of thought upon the dictum of Aristotle. 

But it is now time that we should revert again to our 
example of reasoning, and continue the division of each 
syllogism into its component parts. We have already seen 
that a syllogism consists of three propositions divided into 
the two premises and the conclusion ; we will now examine 
the propositions themselves more closely. In the statement 
** radii of the same circle are equal to one another," we 
see three distinct portions : first, the subject of which we 
are speaking, and of w^hich something is predicated (that 
is, asserted or denied) ; secondly, the attribute or condition 
which is predicated of the subject; and thirdly, the sign of 
affirmation or negation. The technical names for these are, 
the subject, the predicate, and the copula. 

In the proposition above quoted it will be observed that 
the ichole of the subject is spoken of; for when we say "radii 
of the same circle," w^e evidently mean every radius that 
could possibly be drawn. Accordingly, such a proposition is 
termed universal, as the predicate is universally applied to 
every part of the subject. But if we had spoken of a portion 
only of the subject, and had said " some of the radii of the 
same circle are equal to one another," we should have what 
is called a particular proposition, inasmuch as the predicate 

B 3 



f 



10 AN INQUIRY INTO THE 

is affirmed of some particular part of the subject, and not of 
the whole. Thus we see that propositions may be always 
divided into universal and particular, and this distribution is 
said to be made according to quantity. 

Again, '' equality " is predicated affirmatively of ** radii of 
the same circle ;" the sentence is therefore termed an ajjirma- 
tlve proposition : while if the predicate had been denied of 
the subject, thus, "radii of the same circle are not equal to 
one another," it would have been a negative proposition. 
We have, therefore, another system, by means of which to 
classify every possible proposition, and this distribution is 
called a division according to qualiti/. 

And here w^e have introduced to our notice a very im- 
portant branch of Logic, namely, division ; by means of 
which mental process we may at all times obtain a distinct 
grasp of any subject which occupies our attention. Indeed, 
this faculty would seem to be an inherent principle of our 
nature, for whatever may be the science, an attempt has 
always been made from the commencement, to properly 
classify and arrange its various subdivisions ; the best ex- 
amples of such a course being found in such studies as Natural 
History, Comparative Anatomy^ &c. Accordingly, as Logic 
instructs us concerning the principles upon which alone a 
perfect division can be performed, it is an additional proof of 
the necessity which exists for an intimate acquaintance with 
that science. 

We have now glanced quickly, but I trust intelligibly, at 
the structure of a syllogism and its component propositions. 
It remains that we should consider the nature of the materials 
of which the propositions are formed, having already discussed 
the mode of framing them together. The subject of the first 
proposition is, '^ radii of the same circle ;" and in saying this 
we speak of a class, the individuals of w4iich, though they 
may differ among themselves in many respects, yet have some 
features common to all. Thus, one radius of a circle will be 
unlike its fellows as regards position, but it will be exactly 
similar with respect to magnitude. So, when speaking of a 
given circle we mention its '* radius," we employ a name 
that may be apphed to any straight line whatever that is 



VARIOUS MEMBERS OF AN ARGUMENT. 11 

drawn from the centre to the circumference. Such a word 
is called by logicians, a common -name or common-tervi , 
because, as just stated, it is enjoyed in common by a multi- 
tude of objects. But if we proceed to the subject of the 
second proposition, we are met by terms which differ entirely 
from the preceding, viz., **AC and A B," the names given 
to individual radii. These of course can only be applied to 
a single object, and are consequently known as singidar- 
termSy thus serving to distinguish the various members of 
a common-term. 

Let us here pause for a moment to consider the results at 
which we have now arrived, and let us fully comprehend 
the purport of common and singular terms. We see that 
a common -term when applied to an object, merely indicates 
that it possesses certain properties which are shared in like 
manner by all the other constituents of a specified group. 
It is, therefore, evident that such a term or name belongs 
in reality not to an individual, but to a definite" combina- 
tion of qualities which are found in it. And the mode in 
which a common-term is obtained, is by comparing a number 
of separate objects, observing the points wherein they agree, 
combining these points of agreement into one idea, and then 
giving this combination a name, so that at any future time 
we may be able to recall the idea without having the trouble 
to go through the same operations again. Thus, for ex- 
ample, men observed the properties of many natural bodies, 
and finding that a certain number refused more or less to 
alter their volume or shape, the name of solidity was con- 
ferred upon this property ; and, accordingly, whenever we 
hear the term " solid " applied to anything, we at once know 
that the body spoken of will resist a change either as to 
volume or shape. This process of combining various pro- 
perties into one idea is called ahstraction, and is the reverse 
of that previously described, namely division ; for while the 
Litter is al ogether occupied in discovering the points of 
difference between various notions, the former exclusively 
deals with the points of resemblance. 

A singular -term is on the contrary employed to designate 
individuals instead of classes, and therefore is a mere arbi- 



12 AN INQUIRY INTO THE 

trary sign which conveys the notion of one single object. 
Such are all names of persons, rivers, cities, &c., and even 
common -terms may be converted into singular -terms by the 
employment of the demonstrative pronouns, as ** this book," 
" that house," &c. &c. 

There is yet another distinction of the members of a pro- 
position, which it will be needful to notice. We have hitherto 
spoken of the subject and predicate together with the copula ; 
now the two former are called the terms, as when a proposi- 
tion is expressed in logical order they will form its respective 
boundaries or terminations, the copula occupying an interme- 
diate position. 

Of these terms it will be observed that there are three in 
each syllogism ; two forming the subject and predicate of the 
conclusion, while the other is confined to the premises, in 
both of which it occurs. From these positions it is, that the 
names of the respective terms are derived ; thus, the pre- 
dicate of the conclusion is called the major-term, the sub- 
ject of the conclusion is known as the minor-term, and the 
remaining term is characterised as being the middle-term. 
These names, too, are used to distinguish the premises, for 
that proposition which contains the major-term is called the 
major premiss, while the other, for a similar reason, is styled 
the minor premiss. 

We are now in a condition to perceive clearly the full force 
of the train of reasoning which we chose in the first place as 
the subject of our analysis. In the first syllogism, we see 
that a middle -term, " radii of the same circle," is chosen, with 
which are respectively compared the major-term, '^ mutual 
equaHty," and the minor term, '* A C and A B ;" the result of 
this comparison being, that a certain relation, viz., ** mutual 
equality," may be predicated of A and A B. In the second 
syllogism, we have precisely the same major and middle term^, 
but a different minor-term, which, however, is found to bear 
a similar relation towards " mutual equality," as did the other 
minor, ** A and A B." The object then sought to be at- 
tained, is to show the equality of certain portions of the two 
minor-terms, and this is done by employing a fresh middle- 
term to serve as a means of connecting the idea of " equality " 



VARIOUS MEMBERS OF AN ARGUMENT. 13 

with the notion '* A C and B C." This middle -term is " things 
which are equal to the same thing," and when it has been 
properly applied, as in the third syllogism, we attain the de- 
sired result, viz., "AC and B C are equal to one another," or 
" A C is equal to B 0." 

Finally, let us recapitulate the information which we have 
acquired from our rapid survey of the extent of Logic. We 
find that it will be necessary to investigate, first the subject 
of notions or terms ; next, the comparison of terms, or pro- 
positions ; and finally, the deducing a conclusion from the 
juxtaposition of two propositions, or in other words, the 
nature and construction of syllogisms. 

Necessarily this preliminary chapter has been somewhat 
discursive, and has but briefly sketched the more salient prin- 
ciples and branches of Logic. This glimpse of the path 
before him, however, as stated in the Introduction, will pro- 
bably prove of great assistance to the student, for he will now^ 
proceed to a more detailed examination of the science, with a 
good notion of w^hat he may expect to meet; a course which 
is surely preferable to that too often followed, whereby the 
learner is introduced at once to tedious technicalities, without 
the slightest idea as to where he will find himself at the end 
of his study. 



14: 



CHAPTER II. 



OF NOTIONS OR TERMS. 



The student is now about to descend into the plain, and to 
enter upon that road whose various windings and ultimate 
end he has recently sur\eyed from an eminence. Conse- 
quently he will for awhile lose sight of the goal, but as he is 
in a great measure acquainted with the general features of 
his course, he will not be dismayed if the path should not 
immediately appear to tend in the desired direction. And 
here I may mention that at first we shall proceed through 
a region abounding in hard names ; but as the principal 
technicalities of the science have been already introduced, 
together with the principles upon which they are based, 
no difficulty will, I apprehend, be experienced in conquering 
what might otherwise prove a rather formidable array. 

Our immediate subject is, of course, notions or terms ; for 
we must obviously possess a certain number of ideas (logically, 
terms), before it would be possible for us to make any attempt 
whatever at a train of thought or reasoning. Accordingly, 
it might be considered necessary that I should in the first 
place examine the question as to whether ideas are coeval 
with the mind itself, or whether they are the results of ex- 
perience : but, were I to do this, I should quit the domains 
of Logic for those of metaphysics. Suffice it, therefore, if I 
describe the manner in which we obtain certainly many of 
our ideas, and possibly all, 

§ 1. Simple -apprehension. 

Yfhen any object is presented to the mind, and the atten- 
tion is directed to it, a certain mental impression is produced, 
unintelligible indeed as to its nature, but the result of which 



OF NOTIONS OR TERMS. 15 

is that the object is recognised when again observed. That 
is to say, an idea is formed in the mind of that combination 
of properties and appearances which revealed itself to the 
senses upon inspection. Such an idea is termed an intuition, 
or singular -representation, and evidently can only refer to an 
individual object. It is also necessary for purposes of inter- 
communication, that names should be given to these several 
intuitions, and these names are called singular'terms ; such, 
for example, are, "London, France, Charles, Bucephalus." 

Now it is evident that if a separate personal name w^ere to 
be bestowed upon each object, great confusion would result ; 
and as in the majority of cases it is by no means essential 
that, when speaking of an object, reference should be made 
to some particular individual, it would speedily be found 
necessary to assign certain class-names, under which a number 
of similar objects might be grouped. This, accordingly, is 
done in the following manner. 

Suppose a great many individual books had come under 
our notice, and we w'ished to be able to recall at pleasure the 
general idea produced by any one of them, without, however, 
mentioning it by name. In the first place we should com- 
pare several together, and ascertain the points in which they 
resembled, and differed from each other; thus, we should 
perceive that some were ilhistrated and others not ; that one 
related to biography, another to history, and a third to mathe- 
matics ; that there were many gradations of size and bulk ; 
that they were bound in various styles; but also that every 
one of them agreed in possessing certain definite properties. 
These properties we should then proceed to abstract or 
separate from those qualities wherein the volumes differed ; 
and, combining the former into one idea, we should be able 
to conceive of a class of things, each member of -which 
would contain in itself all those viarks or attributes which 
we had selected as essential to the idea in question. Finally, 
we should apply some name, in the present case '* book," to 
the class thus imagined, and in this manner we should ac- 
complish the oliject with whicli we had set out. 

The process which has here been described is that of ab- 
straction ; it will be seen to consist of five steps, viz., com- 



16 OF NOTIONS OR TERMS. 

parison, or placing several objects together in order to judge 
of their resemblance ; reflection, by which we decide upon 
the properties in which they agree or differ ; abstraction, 
w^hich enables us to form the points of resemblance into one 
idea complete in itself; generalisation, or the conception of a 
class w^hose members shall each contain {inter alia) this com- 
pound idea; and denomination, by means of which we im- 
pose a name for the purpose of recalling to our remembrance 
both the class and the idea ; the names thus imposed, being 
known as common terms ; e.g., ^' sea, river, mountain." 

Into these two classes, then, viz., singular and common re- 
presentations, may all our notions be divided ; and as that 
action of the mind which merely consists of forming an idea 
is termed simple -apprehension, so it is said to be incomplex- 
apprehension when we receive a notion of individuals with- 
out observing any relation between them, or compZex-appre 
hension, when we perceive the existence of a class. 

§ 2. Ahstraction of Common-notions 

The faculty of abstraction is possibly the most active anc 
powerful with which the human mind is endowed ; far frona 
remaining quiescent w^lien it has succeeded in forming 
common -notion (or conception as distinguished from intuition) 
by the comparison of separate individuals, it instantly pro 
ceeds to repeat the process on a larger scale. This is done 
by treating a number of classes as so many individuals, an 
then- — when their points of resemblance have been note< 
and combined into one idea — forming a higher class, which 
will include amongst its members all the former classes, 
Nor need we stop even here, for it is evident that no limit 
exists to the number of repetitions of such a proceeding, 
unless indeed there be a limit to the exercise of imagination 
itself. 

Now every science arranges the subjects upon which it 
treats, in a perfectly similar manner, this being based upon 
the results of abstraction : accordingly, logicians have devised 
a certain scheme of names for this system, which we shall 
now explain. 



OF NOTIONS OR TERMS. 17 

A single object is called an individual, and comprehends 
within itself two distinct sets of marks or attributes ; these 
are ; first, that combination of qualities which w^e abstracted 
to form the idea of a class, and, secondly, such attributes as 
remain. Each of the former is termed a ^ro]^erty, whilst 
the latter are called accidents or differences j the class of 
which the individual is a member being known as a species. 
This species, which is merely composed of individuals, is 
Called the lowest or infima species, and the next higher class, 
being founded upon a consideration of infimse species, is 
termed a genus: the latter name, however, is only applied 
when we contrast the higher class with the lower, for in the 
next stage of our conceptions we come to a yet wider genus, 
of which the previous genus is only a species. Thus we go 
on until we arrive at the most comprehensive class of all, 
which is accordingly named the highest or summum genus, 
and this, of course, can never be a species, for there is no 
higher class to include it. Every other genus is called a 
suhaJtern genus, being alternately a species and a genus. 

An example of the above method of arrangement may be 
given as follows : — 

Individual .... Iron. 

Infima species . . . Metal. 

Subaltern genus . . Elementary substance. 

Summum genus . . Matter. 

Accordingly, we can say that iron is a kind of metal ; that 
a metal is a species of elementary substance ; that an elemen- 
tary substance is a genus of which metals are a species, or 
that an elementary substance is a species of matter. 

It is, of course, quite clear that the precise details of the 
sj^stem, such as the question of w^hat are to be considered as 
individuals, or where abstraction is to cease, must be left to 
the arbitrary regulations of each science : the only point here 
insisted upon being the fact that this system is employed in 
every pursuit which engages the human mind, thus showing 
decisively that thought proceeds according to certain fixed 
laws ; which laws it is the province of Logic to explain. 



18 



OF NOTIONS OR TERMS. 



§ 3. Predicahles, Extension, and Intension. 

We have already stated that '* predication" is the affirming 
or denying one thing of another; thus, when I say *^A is B," 
I am said to predicate B affirmatively of A, but were I to 
state that *' A is not B," I should predicate B negatively of 
A. i^ow those notions or terms which ma}^- be predicated 
affirmatively of others are called ^^predicahles,'' and must neces- 
sarily include a greater number of objects than the subjects of 
which they are predicated.^ Thus, a species may always be 
predicated of an individual, or a genus of a species ; and there- 
fore, in accordance with the above -given example, we may say 
" iron is a metal," or '' metals are elementary substances," but 
not " metals are iron/' or '^ elementary substances are metals." 

It will here be seen that in legitimate propositions, the 
subject contains within itself not only the whole of the marks 
or attributes which collectively form the predicate, but also 
an additional series of qualities. For instance, " iron " con- 
tains the common-notion of a ^^ metal," together with those 
peculiar marks which enable us to distinguish it from other 
metals : accordingly, there is a greater number of marks or 
attributes in the subject than in the preijicate, and this kind 
of comprehensiveness is called the intension of a term. But, 
on the other hand, we see that the predicate embraces a 
much larger number of objects than the subject, as a *' metal" 
not only includes everything that is '* iron," but multitudes 
of other things besides, such as ^' gold, silver," &c. ; and this 
species of capacity is known as the extension of a term. Con- 
sequently, a term used in extension comprises only the specific 
properties of a body ; and as it is, therefore, more general and 
less distinctive, it may always be predicated of a term used in 
intension, which consists both of properties and of accidents, f 

§ 4. Division of a Common -notion. 

If we are desirous of completely understanding any sub- 
ject, it is very necessary for us to examine it closely, and the 

* Here, of course, I allude to common-terms, for a singular-term can 
never be predicated of anything but itself; e.^., we can say ''John is 
John," but not " a man {i.e., every man) is John." 

f See page 17. 



OF NOTIONS OR TERMS. 19 

mental process by which we perform this is what I shall now 
consider. It is, in logical language, termed division, and 
consists in viewing every general idea as composed of two 
main sections, viz., the several members or parts of the idea, 
and the tie which connects them together. We then place 
the various parts in regular symmetrical order, such as is 
best adapted to their mode of union, and thus we are enabled 
to study each object separately, both as regards its own indi- 
vidual features, and its relations to the other members 'of the 
system. 

Now the " tie " or " mode of union " wdiich has been here 
alluded to, is altogether arbitrary, and depends upon the 
purpose which we have in view when entering upon the 
study of any subject. Take, for example, the science of 
natural history : Aristotle, looking upon the blood as the 
grand basis of the phenomena of life, divided all animals into 
two great classes, one possessing colourless and the other red 
blood, which done, he proceeded to describe the individuals 
forming these classes ; Ciivier, on the contrary, adopted the 
bony skeleton as his guide in the arrangement of the various 
forms of life ; while Rymer Jones, Vogt, and Siebold have 
respectively chosen the nervous system, the phenomena of 
development, and the relative complexity of organisation, as 
keys wherewith to unlock the vast storehouse of nature. 

But when we have in this manner set apart some portion 
of the subject as a general principle to which we must con- 
stantly adhere, it becomes necessary to se})arate the subject 
into as many parts as may be convenient. This is done by 
observing the marks in which one group or class of objects 
differs from another, and thus dividing the whole of the sub- 
ject into a certain number of genera : each of these genera is 
then examined and similarly divided into lower genera ; and 
so we go on until we can no longer discover any smaller 
groups in a class, but are compelled to enumerate the indi- 
viduals of which it consists. Thus we arrive at a regular 
system of summum genus, subaltern genera, infima species, 
and individuals. 

In order, however, that this process may be properly per- 
formed, logicians have laid down the following rules : — 



20 OF NOTIONS OR TERMS. 

1. The whole subject must be divided : that is to say, the 

various parts taken together must exactly equal the 
genus divided. 

2. The division must be conducted according to some 

single, definite principle. 

3. The parts must be quite distinct; no two containing 

any common object. 
Thus, if we w^ere studying architecture, and w^ished to ob- 
tain a correct idea of the class of objects which are termed 
buildings, we must discuss the whole of the subject, and not 
confine our attention to a few species, such as palaces and 
temples only. And then when commencing the division, we 
must proceed according to some settled principle, such as, for 
instance,*^ application," consistently with which we should form 
the different species of " private-dwelHng-houses," ^' factories," 
" warehouses," " churches," &c., and therefore no confusion 
would result, for the third rule given above would remain 
uninfringed. But if we were to pursue a different plan, and 
to divide buildings indiscriminately into *' palaces," *' Doric," 
** Gothic," ** prisons," &c., we should violate both of the latter 
rules, having employed two principles of division, viz., " style" 
and " application," in consequence of which the various classes 
would be intermingled, and no true division would be per- 
formed ; for it is evident that some palaces might be Doric 
and others Gothic, &c. This error is termed cross-division, 
and is one of the most frequent sources of confusion and per- 
plexity in discussion and argument. 

§ 5. Positive, Negative, and Privative Terms, 

In order to test a division as to whether it be perfect, logi- 
cians are accustomed to take each part separately, and ex- 
amine the possibility of dividing the whole subject into 
positive and privative portions with reference to the selected 
part. Thus, suppose the subject " man " be divided according 
to the principle of *' colour :" we should have the four species 
of** white-men," "black-men," "red-men," and "yellow-men." 
We then see that it is possible to also divide " man " into the 
two ideas or conceptions of " whitemen " and "non-whitemen," 
for black, red, and yellow may all be described as non- white. 



i 



OF NOTIONS OR TERHS. 21 

In the same manner *' man " may be divided into '' black " and 
"non-black," ^^ red" and ** non-red," '* yellow " and *' non- 
yellow," and so at length we see that none of the classes in- 
termingle with each other. 

The term " white -men " is called posiVire, because it denotes 
that a certain view (white) is taken of the object (men), while 
the term " non-w^hitemen " is said to be privative , in conse- 
quence of its implying that such a view might be, and yet 
is not taken. If, on the other hand, it were impossible to 
form a certain notion of a subject, the term which implies 
this, such as, for instance, a ''non-white negro," w^ould be 
styled negative, 

§ 6. Definition, 

In the process of logical division it is evidently necessary 
that we should employ some means of precisely determining, 
first, the full extent of the subject to be divided, and then 
the respective capacities of the various parts or species : this 
we are enabled to do by the use of definitions, that is, certain 
expressions which describe an object or notion in such a 
manner that we are enabled to distinguish it from all others. 

Now the act of forming these expressions is termed the 
process of definition, and consists in an enumeration of the 
various attributes composing a notion. As a notion, how- 
ever, may be either singular or common, we are obliged to 
use two kinds of definition, one of which, accidental'definition, 
is applied to individuals, and consists of the specific name 
together with the accidents ; while the other, essential -defini- 
tion, being applied to classes, consists of the generic name, 
together with the specific difference. Thus, the Thames 
might be defined as '' a river which flows through London," 
where " a river " is the name of the species, and " flowing 
through London" the accident which distinguishes the 
Thames from other rivers. Again, we may define light as 
" a species of motion affecting the optic nerves in such and 
such a manner," the genus being " motion," and '' affecting 
the optic nerves" the difference which distinguishes light 
from other species of motion. 

This latter kind of definition, consisting of the genus and 



22 OF NOTIONS OR TERMS. 

specific difference, is also termed logical'deJiniHon.^ in opposi- 
tion io pliij steal 'definiUon, which enumerates such parts of the 
object as are actually separable : e.g., the boiler, mechanism, 
(fee, of a steam-engine. Some writers also include physical- 
definitions under the head of essential-definitions. 

Various rules have from time to time been given by 
logicians for the purpose of securing correct definitions, and 
may be summed up as follows. 

1. The definition must be of exactly the same extent as 
the object defined : that is to say, it must not be of too 
narrow or too wide an application. Thus, to define "gravity" 
as *' a force which attracts bodies to the earth " would be too 
narrow, as not inchiding the celestial attractions, and being 
only applicable to terrestrial gravity : to define it as '* a 
force which attracts one body to another," would be too 
wide, in consequence of its including magnetic attraction, &c. 

2. The definition must not contain anything beyond what 
is absolutely essential to the subject. For instance, it would 
be incorrect to say that a ^*man" is ''an animal endowed 
with the faculty of speech and ivith life,'' as it might then be 
supposed that the existence of an animal with speech, but 
lifeless, was possible. 

3. The definition must be plainer than its subject, and must 
not be a repetition of the same term : e.g., the explana- 
tion that *' a metal " is " a metallic substance,*' would be no 
definition at all, while to assert that it is '* a product of 
Plutonic action " is equally unsatisfactory. 

§ 7. Names and their Divisions, 

We have already seen that when an idea or conception is 
gained of any object or class of objects, some name is imme- 
diately attached to it, for the purpose of recalling the impres- 
sion at any future time. It now remains to describe the 
various species into which these names are divided for logical 
purposes, 

1. Making a division according to logical quahty, we find 
that all names or terms may be divided into positive, privative, 
and negative, which have been described above. Positive 
terms, however, are also called definite, from their distinctly 



OF NOTIONS OR TERMS. 28 

defining an object; while for the reverse reason privative and 
negative terms are styled indefinite. 

2. Names, as regards the method of using them, are either 
univocal, equivocal, or analogous ; that is to say, some have 
only one meaning, such as '' book," ''sofa ;" others have several 
meanings, such as '' light,*' which signifies either the contrary 
of '' heavy," or a physical force ; while others, again, are ex- 
tended from one object to another in consequence of some 
similarity — thus, ^' tongue " may be applied either to the body 
or to a piece of land. 

3. Viewed as to their mutual dependence, terms are ahsolute 
or relative. The former appellation is bestowed upon those 
terms which are considered by themselves as a whole ; the 
latter belongs to those which form part of a more complex 
idea. For example, the term " man " would be absolute ; 
while plaintiff would be relative, as being a portion only of 
the idea plaintiff-and-defendant. It will therefore be seen 
that relative terms exist in pairs, and cannot be applied to 
the same object, as then they would be what is called opposite, 
to distinguish them from compatible terms, as those are 
named which may be so appUed. 

Correlatives is a name given to each pair of relative terms, 
and implies their mutual connection. 

4. Terms are either concrete or abstract, according as they 
imply a notion together with the object furnishing the notion, 
or the notion by itself. Thus " fluid " is a concrete, *' fluidity'* 
an abstract term. 

Also when the terms employed are common terms, or the 
names of classes, a further distinction will be observed. Take, 
for example, the concrete term ** fluid;" it is evident that there 
is here implied a substance possessing certain attributes ; ac- 
cordingly, such a term is called attributive, or coniwtative, 
because it connotes some attributes together with the object. 
Again, the abstract term *' fluidity " is, in like manner, named 
absolute, or non-connotative, from its merely denoting an 
attribute and nothing beyond. 

§ 8. Opposition of Terms, 
There is said to be a contradiction in terms, or two terms 



24 OF NOTIONS OR TERMS. 

are said to be in contradictory opposition to one another, when 
the only difference between them consists in the respective 
presence and absence of a negative particle ; this difference, 
enabling us to apply them universally. Thus, everything' 
must be either "living" or ** not living," "red" or "not 
red," &c. 

When, however, two terms differing as to the same idea 
cannot be both applied to the same object, and yet there are 
some objects to which neither can be applied, such terms are 
said to be in contrary opposition to one another : e.g.^ a man 
is not at the same time " walking " and " running," but a tree 
does neither. 

§ 9. Structure of Terms. 

An idea or term is expressed by a word or words ; thus, 
" man," " horse," " steam-engine," " the Emperor of Russia," 
and such words as can be used alone to represent a term, are 
C2i\[Qdi categorematic ^ while all others are denominated sj/ti- 
categorematic. Sometimes, however, w^e meet with a single 
word apparently filling the place of a term, but for which it 
is necessary to substitute some other expression before its 
full import is conveyed. Take, for example, the sentence 
" He loves ;" this, if reduced to logical form, would be " He is 
a person w^ho loves." 

§ 10. Conclusion and Recapitulation, 

We have now reached the end of our investigation into 
the first great division of Logic, and before we proceed any 
further, it will be well for us to cast a brief glance backwards, 
and fully comprehend the connection which exists between 
the subjects just discussed, and those to come. 

The course, then, of our investigations has been first to 
analyse the method in which we gain and record the im- 
pressions or ideas produced by the various objects which 
attract our attention : in doing this we found that all our 
ideas are either of individuals or of classes, the former 
being the result of incomplex-apprehension, the latter of 
complex-apprehension, which consists of the five processes ofi 
comparison, reflection, abstraction, generalisation, and deno 



OF NOTIONS OR TERMS. 25 

mination. In the next place we examined the mode of 
arranging and classifying our ideas by the abstraction and 
division of conceptions (common-notions) : this led ns to per- 
ceive that the subject of a proposition embraces more marks 
or attributes than the predicate, while the predicate compre- 
hends a greater number of objects ; that is to say, the subject 
has the greater intension, the predicate the greater exten- 
sion. We then showed how a logical division might be 
tested by the use of positive and privative terms, which done, 
it became our duty to describe the process of definition, and 
to explain the v^irious rules which have been laid down for 
the purpose of securing correct results. Finally, we enu- 
merated the divisions of the various names which have been 
bestowed upon ideas, and concluded by noticing the opposi- 
tion and structure of terms. 

It will of course be understood that in order to form an 
idea, it is not necessary tliat a tangible, corporeal object 
should be presented to the senses, for we have many notions 
to which there exists no corresponding reahty : such, for ex- 
ample, are our ideas of justice, honesty, &c. In fact it may 
be said that no common-notion whatever has any existence 
out of our own minds ; the conception of ^^man" for instance 
being merely that of a combination of marks or attributes 
which are never found separately by themselves, but are 
always united to other objects. Thus it is certainly true that 
the idea ^^ man'' has no isolated existence, but still it cannot 
be denied to exist, simply because it does so in conjunction 
with something else. 

This question, here touched upon, is the celebrated bone 
of contention between the schools of the nominalists and the 
realists, the former following Abelard, and denying that 
common-notions (or universals) are anything more than mere 
names, while the latter, under the guidance of Plato, strongly 
affirmed the reality of their existence. The days of the 
schoolmen was the time when this controversy grew most 
warm, and such was the importance attached to the subject, 
that kings and popes did not scruple to exert their utmost 
power in the attempt to secure the triumph of the sect which 
they respectively patronised. But this by the way. 

c 



26 OF NOTIONS OR TERMS. 

Now when the mind has once become supplied with ideas, 
it is enabled to reflect, the result of which is the formation of 
certain judgments. These judgments, when formally stated, 
are termed in logical language propositions } and, accordingly, 
the subject of our next chapter will be an examination of 
their origin and nature. 



27 



CHAPTER III. 

OF JUDGMENTS OR PROPOSITIONS. 

§1. Formation of Judgments, 

Judgment is the act of determining by comparison whether 
one idea is or is not inckided within another ; that is to say, 
it ascertains whether an individual belongs to a certain 
species, or a species to some genus. Archbishop Thomson 
has defined it as '^ an attempt to reduce to unity two cogni- 
tions." He says, *^When one decides that ' Socrates is wise/ 
it is that hereafter one may, by combining the two notions, 
think of * the wise Socrates.' " Now it is by no means evident 
that the two cognitions are here attempted to be reduced to 
unity, for no person would surely expect to render them so 
inseparable, that whenever the idea of '* wisdom " presented 
itself to his mind it should be invariably accompanied by the 
notion of "■ Socrates." In fact the judgment that *' Socrates 
is wise," is merely an assertion that '• Socrates belongs to the 
class or species of wise men," or " Socrates possesses wisdom," 
thus enabling us to fix his place more exactly in our system 
of ideas.* 

Accordingly, it will be seen that judgment is the result of 
that mental faculty which so strongly impels us to classify and 
arrange the various notions with which our senses provide 
us, so that we may the more clearly comprehend the various 
dependencies and relations by which they are connected to- 
gether into one harmonious whole. We have already con- 
sidered three portions of this faculty, viz., abstraction, division, 
and definition ; it now remains to consider judgment, without 
which none of these processes could be conducted. 

* For further information upon this point, see Appendix A. 
c2 



28 OF JUDGMENTS OR PROPOSITIONS. 

And here it might well be asked whether, if the formation 
of common-notions is the result of judgment, a judgment also 
in its turn is not the result of reasoning — for we have already 
seen that the conclusion of a syllogism is a judgment or pro- 
position. This question, however, belonging as it does to 
metaphysics, cannot be satisfactorily answered in the present 
place ; and, therefore, I shall at once proceed to discuss the 
nature s^nd proximate origin of propositions, without minutely 
investigating their remote ancestry. 

§ 2. Categorical Propositions^ 

A categorical judgment or proposition is an assertion that 
one idea agrees or disagrees with another, and consists of 
three parts — the subject or idea under examination ; the 
predicate, or idea to which the subject is referred ; and the 
copula, which determines the relation between them. Thus, 
in the proposition " lions are animals," the subject is " lions,'* 
and is connected to the predicate *' animals,*' by the copula 
'^ are," which implies that '' lions " form a species of the genus 
'^ animal." This judgment results from our having compared 
the two ideas with a view to ascertain whether the attributes 
of " animal " were contained in '^ lion." 

The subject and predicate of a proposition, may of course 
be infinitely varied, since there is no limit to the number of 
ideas; but the copula always remains the same, being either 
*' is," or 'Ms not," or their equivalents. And here it may be 
remarked that the word '' is " signifies, when employed in a 
proposition, the identicality of the subject and predicate, such 
identicality being, however, limited by the form of the propo- 
sition. The subject and predicate are also called the terms of 
the proposition, as they form its boundaries or terminations. 

Categorical propositions are divided mio pure diXidi modal — • 
the former being cases where the subject is directly asserted 
to agree or disagree with the predicate ; the latter where the 
'subject is said to agree or disagree with the predicate in some 
particular manner. For instance, " The sea is rough ;" " He 
addressed the people ;" are both pure, but '*The sea is terribly 
rough ;" " He addressed the people good humouredly ;" are 
modal. This distinction is, however, of no use for logical pur- 



OF JUDGMENTS OR PROPOSITIONS. 29 

poGes, since we may always treat modal propositions as being 
pure, by simply attaching the mode to either the subject or the 
predicate : thus, in the example above given, " terribly rough " 
must be taken for the predicate. 

§ 3. Hypothetical or Conditional Propositions, 

All judgments are not formed by a comparison of existing 
notions, for it is possible to decide npon the mutual relation 
of two assumed conditions of things. Accordingly, we meet 
with a class of propositions termed hi/pothetical, or conditional, 
whose assertions are subject to a certain condition : of this 
kind are such sentences as the following — " If the results of 
geological science are trustworthy, the earth has existed for 
countless ages." '^ If you do this well, you shall be rewarded." 

Hypothetical propositions are not, however, to be considered 
as different in nature from categoricals, for both species of 
judgment result from precisely the same operation of the 
mind. This will be clearly seen if we examine one of the 
instances given above, and ascertain what it is that we really 
assert. Taking the first example, it is evident that we decide 
nothing as to the results of geological science, or as to the 
earth, but we say that the assuming those results to be trust- 
worthy would necessitate our granting the earth to be of the 
age stated. This judgment, then, may be expressed as 
follows, viz., ^' The case or supposition of the results of geolo- 
gical science being trustworthy, is a case or supposition of 
the earth having existed for countless ages " — where the 
subject, copula, and predicate of a categorical proposition will 
be at once recognised. 

§ 4. Disjunctive or Alternative Propositions, 

There is yet another form which our judgments may 
assume, this being the statement of some alternative, such as, 
** Either Tyndall is wrong, or mechanical force produces 
heat ;'• — which, accordingly, is known as a disjunctive or alter- 
native proposition. To show its harmony with the forms 
already discussed, w^e have only to remark that it may be 
converted at w^ll into a hypothetical, as, " If Tyndall is not 



30 OF JUDGMENTS OR PROlPOSITIONS. 

wrong, mechanical force produces heat ;' — or into a categori- 
cal, thus : ^* The case of Tyndall being wrong, and the case of 
mechanical force producing heat, are all the cases possible." 

As regards hypothetical and disjunctives considered apart 
from categoricals, we shall have more to say when we come 
to discuss the treatment of arguments where they occur ; at 
present, however, we are concerned altogether with pure cate- 
goricals, having shown that all propositions whatever may be 
regarded as such. 

§ 5, Quantify/ of Propositions, 

As we have no ideas beyond those of individuals and of 
classes, our judgments must always be concerning intuitions 
(singular-notions), or conceptions (common-notions). Now a 
singular-notion being indivisible, we must invariably treat of 
the whole of it ; but as regards common-notions, we are able 
to discuss either a part or the whole. This distinction has 
enabled logicians to divide all propositions according to 
qiiantity.; that is to say, according to the extent of their 
subjects : and, therefore, whenever the subject is a singular- 
notion, as, '^ John is rich," — or the whole of a common-notion, 
as, '^ All metals are conductors of heat,"- — the proposition is 
called universal } but if only part of a common -notion be 
employed for a subject, as, ^'Some metals are lighter than 
water," then it is termed particular. 

§ 6. Quality of Propositions, 

Another division of propositions is according to the signi- 
fication of the copula, which is termed the quality of a judg- 
ment, and as this must be either affirmation or negation 
('* is " or *' is not "), so propositions are styled affirmative or 
negative, according as they respectively express the agree- 
ment or disagreement of subject and predicate. Thus, " The 
whale is a mammifer" is an affirmative proposition ; while 
" No alloy of ammonium is stable " is negative. 

It must here be remarked that a negative sign may occur 
in a proposition, and yet not belong to the copula ; in such a 
case the proposition is affirmative. Take, for example, this 



OF JUDGMENTS OR PROPOSITIONS. 31 

judgment, "Not to accept the offer is great folly," and we see 
that the *' non-acceptance " and " great folly " are declared to 
agree with each other. 



§ 7. Distribution of Terms, 

Whenever in a judgment a term is used in its full sense — 
that is to say, as comprehending every single object that it 
could possibly include — it is said to be distributed: accord- 
ingly, every universal proposition distributes its subject, but 
particulars do not. When, however, we examine into the 
distribution or non-distribution of the predicate, we find that 
this depends not on the quantity, but upon the quality of the 
proposition. Thus in negative judgments it will be seen 
that the lohole of the predicate is declared to disagree with 
the subject ; as, for instance, in the following proposition, '' No 
negro kingdom is civilised," where the entire idea of " civili- 
sation " is pronounced to be incompatible with the idea of 
'^ negro kingdoms." But in affirmative judgments the case is 
different, as we can only infer from the form of the expression, 
that ^ part of the predicate is implied. Tims, knowing that 
one ^or^/o?2 of the genus "animal" is composed of "horses," 
or in other words, that the attributes forming the idea of 
'' animal" is to be found in every horse, we can say correctly 
that " horses are animals." Here, then, the predicate is not 
distributed. 

Consequently, w^e arrive at these two rules : — 

1. The subject is distributed in universal, but not in 

particular propositions. 

2. The predicate is distributed in negative, but not in 

affirmative propositions. 
The latter rule is, however, subject to three exceptions ; 
first, when in an affirmative proposition the predicate is a 
singular notion and is consequently distributed, for w^e can- 
not think of a part only of an intuition ; secondly, when some 
expression is employed which indicates that the icliole of the 
common-notion forming the predicate is compared with the 
subject. Thus, in both of the propositions, '^ Davy was the 
discoverer of potassium," and " These fragments are all that 



32 OF JUDGMENTS OR PROPOSITIONS. 

remain,"' — the predicate is distributed. The third exception 
is to bo found in negative propositions, where the predicate 
is qualified in such a manner as to indicate that part only of 
its signification is employed. This will be observed in such 
sentences as '* Steam-engines are not some machines ;" ** No 
men are some created beings ;"— which import respectively 
that some machines are not steam-engines, and that some 
created beings are not men. These latter propositions are 
termed payiial-negatwes, those to which the rule apphes 
being styled total -negatives. 

§ 8. Relation of Terms, 

We have already stated that judgment is the act of deter- 
mining by comparison, whether one idea is or is not included 
within another. In doing this we find some cases where the 
notions are of equal extent, such as the various intuitions 
produced by the same object under different circumstances, 
or those conceptions which comprise the same individuals. 
This fact we express in the form of the proposition, which 
consequently indicates that it is the result as it were of two 
judgments, the one having ascertained that the subject of 
thought belonged to a certain class, while the other deter- 
mined that it was co-extensive with the class. Such propo- 
sitions are those mentioned above as constituting exceptions 
to the rule which declares that no affirmative proposition dis- 
tributes the predicate. 

Now in consequence of this relation, it follows that we may 
indifferently affirm the predicate of the subject, or the subject 
of the predicate. Thus it matters not whether we say 
'' Davy was the discoverer of potassium," or '* The discoverer 
of potassium was Davy ;" or again, whether we say, '^ These 
fragments are all (the fragments) that remain," or *' All the 
fragments that remain are these (fragments)." Accordingly, 
such propositions are termed substitutive, from our being able 
to employ subject and predicate as substitutes for each other. 

All other affirmative propositions have their predicates 
n on -distributed, and merely import that these may be attri- 
buted to, and not substituted for, the subjects. On this 
account they are styled aitributive. 



OF JUDGMENTS OR PROPOSITIONS. 33 

§ 9. Systematic Classification of Propositions, 

Having now given a full description of the various divisions 
and subdivisions of propositions, it will be well to give a short 
summary of the system. This is best done by the use of a 
** scheme," as follows : — 

Propositions 

regarded logically, i.e, with reference to their form, 

are divided accordinor to 



1 

Quantity, 


1 
Quality 


r, 


into 
1 




into 

1 




i 1 
ersal. Particular. 


Affirmative : 




Negative : 




these being sub- 




these being sub- 




divided as regards 




divided as regards 




the relative extent 




the distnbution or 




of subject and 




non-distribution of 




predicate, 




the predicate, 




into 

1 




into 
1 



I 

III! 

Substitutive. Attributive. Total. Partial. 

§ 10. Tahle of Possible Propositions, 

We see by the above scheme, that propositions are of 
four great classes, afSrmative-substitutive, affirmative -attri- 
butive, total -negative, and partial-negative. Each of these 
may be again subdivided into universal and particular, so 
that altogether there are eight possible kinds of judgment or 
predication. The names of these propositions, however, being 
too long and cumbersome for constant repetition, logicians 
have adopted certain letters to serve as symbols for these 
names, and in the following table will be found a list of all 
possible propositions, together with their respective symbols, 
and illustrative judgments ; the subject and predicate in each 
being represented by the letters X and Y. 

c 3 



34 OF JUDGMENTS OR PROPOSITIONS. 



Name. 


Example. 


Svmbol 


Univ. Affirm. Substi. 


All X ia all Y. 


' U. 


Univ. Affirm. Attrib. 


All X is some Y. 


A. 


Univ. Total Neg. 


No X is Y. 


E. 


Univ. Partial Neg. 


No X is some Y. 


V' 


Part. Affirm. Substi-. 


Some X is all Y. 


Y. 


Part. Affirm. Attrib. 


Some X is some Y. 


I. 


Part. Total Neg. 


Some X is no Y. 


0. 


Part. Partial Neg. 


Some X is not some Y. 


lO. 



In tins table there are two propositions which, as being of 
little practical importance, we may leave out of our future 
consideration. I allude to those whose symbols are y] and w ; 
the reason of their inutiHty being as follows. "When we say 
*^ no men are some animals " (17), we mean *' some animals are 
not men " (0), wdiich latter, being a much more forcible and 
convenient mode of expression, is usually adopted. Also 
when we say '' some men are not some animals " (w), the 
power of negation is still less, for there is nothing to prevent 
us saying at the same time ^* some men are some animals." 

Accordingly, I shall confine my future remarks to the six 
kinds of judgment, U, A, E, Y, I, and 0, and when the 
student is able to treat arguments involving these, he will 
find very little difficulty in disposing of those rare cases in 
which r) and w may occur. 

§ 11. Interpretation of the Copula. 

The copula, as already stated (§ 2), signifies a certain 
identicality of the subject and predicate. This identicality, 
however, may be considered from several points of view% ac- 
cording to the purpose we have in hand. Thus, if we were 
engaged in determining the intension of the notion " fluids," 
i.e. in ascertaining what were its marks or attributes, and w^e 
w^ere to form this judgment, '^All fluids are compressible," we 
should mean that fluids were contained in the class of com- 
pressible substances, in virtue of one of their attributes being 
compressibility. But if we were chiefly desirous to fix the 
relative extent of the terms, i.e. to determine their extension, 
we should only care to imply by the above expression that 
the class of compressible substances included amongst other 
things the class of fluids. 



OF JUDGMENTS OR PROPOSITIONS. uO 

It will, however, be observed that these are not two different 
meanings of the proposition, but merely two different modes of 
regarding the same meaning. 

Another method of interpreting the copula, or connection 
between subject and predicate, has been suggested. This 
consists in viewing the judgment as regards its denomination, 
i,e, in considering it as implying that the predicate may be 
given as a name to each of the objects contained in the 
subject. The example stated above, if interpreted in this 
manner, would be held to imply that the name ^^ compres- 
sible " might be given to every fluid. 

§ 12. On some other Properties of Judgments. 

It is impossible for us to form a complete idea of any object, 
as we are unable ever to ascertain the whole of its various 
marks or attributes. Accordingly, we observe continually 
some new feature, and this it is which causes us to make so 
many fresh judgments. At the same time there always exists 
a certain set of marks which are almost inseparably connected 
in our minds with resj^ective ideas; so that it is scarcely 
possible to recall these ideas without at the same time recall- 
ing those attributes. Take, for example, the case of material 
bodies ; we cannot think of any, without also thinking of 
shape and extension, two properties of matter. 

Upon these considerations, metaphysicians, and after them, 
logicians, are occasionally accustomed to consider judgments 
with reference to their bearing upon our knowledge of the 
subject. If they increase our information, such as those 
which result from our discovery of some new attribute, they 
are termed ampliative. If they add nothing to what we 
really know, they are called explicative when they are in a 
measure explanatory of the subject by predicating some 
closely-connected attribute: or tautologous, when the predicate 
is identical with the subject, such as, '' A man's a man." 

§ 13. Concluding Remarks. 

In the present chapter we have taken the subject of 
*' judgments," for logical investigation, and the result of oar- 
studies may be summarised as follows. 



3G OF JUDGMENTS OR PROPOSITIONS. 

Judgment is the act of determining the agreement or dis- 
agreement of two notions, and when its result is expressed in 
words, it forms a sentence which is termed a proposition. 
Propositions may be stated categorically, such as *' A is B," or 
*^ A is probably B," the former being piire, the latter modal : 
hypothetically, such as *^ if A is B, is D :" or disjunctively, 
such as *^ either A is B, or C is D." All propositions may, 
however, be reduced at pleasure to a pure categorical form. 
Accordingly, in a systematic account of judgments, reference 
is made exclusively to pure categoricals, concerning which 
there are four great doctrines. The first is of quantity, and 
divides all propositions into universal or particular, according 
to the respective extent of their subjects. The second is of 
quality, and divides all propositions into affirmative or nega- 
tive, according to the import of their copulse. The third is 
of distribution, and determines in what cases the various 
terms are employed as wholes or parts, t.e., whether they are 
distributed or non-distributed. The fourth is of relation, 
and arranges all propositions according to the extent of their 
predicates ; affirmatives being divided into substitutives and 
attributives, and negatives into total and partial. From this 
classification it results that there are eight different kinds of 
propositions, each being for the convenience of logicians 
distinguished by an arbitrary symbol. Two, however, of 
these species may be dispensed with as being of little prac- 
tical importance ; and, therefore, only the remaining six need 
be dwelt upon in future. Judgments may also be viewed as 
regards the significance of their import, which varies with 
the method of interpretation. Thus, they may be considered 
with reference to their intension, or attributes of the subject; 
extension or relative capacity of the predicate ; denomina- 
tion, or applying the predicate as a name to each member 
of the subject ; or, finally, with reference to their bearing 
upon our knowledge, according to which they are ampliative, 
or informing; exphcative, or explanatory; tautologous, or 
useless. 

We are, therefore, now in a position to enter upon the in- 
vestigation of a most important and interesting topic — the 
formation of new judgments from a consideration of some 



OF JUDGMENTS OR PROPOSITIONS. 37 

already existent. This process, termed reasoning, is as it 
were, the very climax of logical science, and illustrates the 
use of our preceding reflections upon terms and judgments. 
Its study is, however, far from being difficult when orderly 
arranged, and is calculated to induce the most pleasing emo- 
tions in the mind of any person who has attentively pursued 
it, and has observed the singular simplicity and harmony 
with which the mind works. In fact, we have already had 
some remarkable instances of this, for we have discovered 
that the vast, nay infinite world of ideas — than which nothing 
can be more varied and diverse — may be referred to a few 
simple processes of the intellect, and may be grouped together 
into a system of surprising lucidity. The same thing occurs 
with our innumerable judgments, which, though outwardly 
dissimilar and confused, are found to be all constructed on 
the same 2:)lan, and to be capable of arrangement in orderly 
sequence and regularity. 

Accordingly, to him who zealously strives after a complete 
understanding of these facts, there accrues an elevation of 
the mind such as cannot otherwise be attained. That grand 
principle of systematic grouping which underlies all his 
capacities of acquiring knowledge, is roused into vigorous 
and healthy exercise ; his powers of observation, or rather, 
his capabilities of impression by outward objects, are greatly 
increased ; and, while he is charmed by the stately vista of 
theoretical truth which reveals itself before him, he is at the 
same time conscious that his toils have not been unfruitful in 
practical results. 



38 



CHAPTER IV. 

OF REASONING OR ARGUMENT. SYLLOGISMS. 

§ 1. Measoning in General, 

The desire of the mind for knowledge admits of no satiety : 
vast though its acquisitions may be, the pursuit is in nowise 
slackened ; and the regions of infinity itself oft yield rich 
spoils to some aspiring intellect, which, thirsting for new 
worlds to conquer, has striven to investigate the most mys- 
terious recesses of the universe. This fact is proclaimed in 
every page of the world's history : the speculations of the 
philosopher, the actions of the statesman, the harmonious 
breathings of the poet, all alike bear witness that the watch - 
w^ord ^* progress " is stamped indelibly upon the human mind. 
If, then, we consider that in our souls there is implanted a 
faculty w^hich irresistibly carries us forward to the acquire- 
ment of new truths, we shall not be surprised w-hen we 
discover that there are also implanted certain natural laws, 
w^hich serve to control and guide that faculty in the manner 
best adapted for the attainment of its ends. Accordingly, 
since these laws exist, and are the same in all minds, it results 
that the method of acquirin*g knowledge is identical in every 
case. 

Now, information may be obtained in three different ways : 
by the presentment to our minds of the various objects of 
thought, thus inducing the formation of ideas ; by the com- 
parison of ideas, which enables us to make judgments ; and 
by the comparison of judgments for the purpose of arriving 
at some new truth. The two former of these processes have 
hitherto engaged our attention exclusively ; we have there- 
fore now to investigate the latter, which, of all the mind's 



OF REASONING OR ARGUMENT. SYLLOGISMS. 39 

actions, challenges our observation in the most marked 
manner. 

Reasoning, then, consists in arriving at some new truth, 
from a consideration of other truths already estabhshed. 
These truths it is evident may be expressed in numberless 
ways, as also may the truth to be inferred ; but whenever 
an act of reasoning is put into words, it will always be 
found possible to separate it into two portions, one expressing 
some admitted truths, the other some truth resulting from 
them. Thus the mere arrangement of the argument (as an 
act of reasoning when expressed in words is termed) matters 
nothing with regard to the principles involved ; and, conse- 
quently, in spite of these principles being, as above stated, 
universal, we everywhere find that reasoning is expressed in 
whatever manner may be suggested by the circumstances of 
the case. This it is, which has led to such erroneous opinions 
as to the true office and nature of Logic ; men, distinguished 
in other respects for their prodigious intellectual power {e.g. 
Locke), having imagined that because Logic alters the loose, 
popular arrangement of arguments, into a form better adapted 
for elucidating the principles concerned, it therefore is oc- 
cupied in teaching some particular method of reasoning, the 
laws of which are different to those employed by such as have 
not studied the science. 

§ 2. SjjUogisms. Inference. 

From the preceding remarks it will have been gathered 
that before entering upon a logical investigation of any act 
of reasoning, it is necessary that this should be expressed in 
a certain regular form. Such forms are termed syllogisms, 
and are so constructed as to show the validity of the argument, 
without any reference to its matter^ i.e., to the subjects of 
which il treats : that is to say, the mere manner of expression 
is such that the new truth, or conclusion, is at once seen to 
be legitimately deduced from the truths already granted, viz., 
the premises. 

The act of thus deducing the conclusion from the premises 
is termed inference, and consists in ascertaining the full pur- 
port of the premises. Thus, ascertaining that chlorine is a 



4-0 OF REASONING OR ARGUMENT. 

gas, and knowing that all gases are elastic, I infer, or conclude 
that chlorine is elastic. If expressed in logical form, the 
argument would run thus : ** All gases are elastic ; chlorine 
is a gas ; therefore chlorine is elastic." It is not, however, 
always the case that we commence our reflections with the 
premises, for we frequently first consider the conclusion, 
under the guise of a question or problem. For instance, 
suppose in the above case that we wished to know whether 
chlorine was elastic or not : we might ascertain the truth by 
examining the substance ; and, finding it to be a gas, we 
should be certain that it was elastic, as previous investiga- 
tions had decided that all gases were so. Here we see that 
there are two terms, '^ chlorine," and *^ elastic," the agreement 
or disagreement of which, we were enabled to decide upon 
by finding some third term, " gas," wherewith they might be 
respectively compared. This third term is called the middle 
term, and is the very essence of the syllogism ; the inference 
connected with it being accordingly terra ed syllogistic, or 
mediate inference. 

We now arrive at a somewhat interesting question, viz., 
whether there can be any kind of reasoning other than 
mediate inference ; that is to say, can we from one judgment 
or truth only, directly infer some other ? Some writers have 
contended that such a thing is possible, and have accordingly 
described a species of reasoning which they term immediate 
inference. Others have denied the possibility of this, and 
assert that in the examples adduced by their opponents, there 
is no inference or reasoning whatever. 

Now the truth would appear to be that the disputed cases 
are in reality certain examples of mediate inference, which 
possess such strongly marked peculiarities as to distinguish 
them from all other instances of reasoning, and to lead to the 
belief that the laws upon which they are constructed differ 
from those of the regular syllogism. 

It will, therefore, be w^ell to consider these arguments apart 
from the great bulk of reasonings, more especially as owing 
to the above mentioned views being adopted, logicians have 
devised rules for the treatment of such cases, to which rules 
both parties agree. The arguments themselves may be 



SYLLOGISMS. 41 

classed under three great heads or doctrines, viz., opposition, 
conversion, and coincident junction : these I shall now pro- 
ceed to investigate, showing in each case the real nature of 
the argument. 

§ 3. Opposition. 

The relation which exists between any two propositions 
differing in form, but identical in matter, is termed opposi- 
tion. Thus, the judgments '^All fishes swim," and '^ No fishes 
swim," agree as regards their matter, i.e., their subjects and 
predicates are respectively formed by the same notions ; but 
they differ with respect to form, one being A, or universal- 
affirmative -attributive, while the other is E, or universal-total- 
negative : they are accordingly said to be opposed. And 
here it should be remarked, that in order for opposition to 
exist, the respective subjects and predicates must, in both 
propositions, be considered with reference to the same ideas, 
time, and circumstances. Thus, I might say, " This man is 
happy," and '* This man is not happy," with perfect truth, 
providing I were alluding to his condition at separate times ; 
but otherwise, the judgments would be opposed to each 
other. 

The doctrine of opposition is based upon an examination 
of the various forms of propositions, and declares the natural 
laws which regulate their mutual relations. Take, for ex- 
ample, a proposition in E, " No metals are vaporisable." On 
analysing this, we arrive at the following results: that the 
proposition asserts the total exclusion of the class ^' metals " 
from the class of "vaporisable substances;" that — since from the 
nature of things we know there must always be either a total 
exclusion, or partial inclusion at least of one class in another — 
accordingly, if the proposition be true, any judgment which 
asserted an inclusion (even if only partial) of '' metals" within 
" vaporisable substances," would be false ; while if the proposi- 
tion were not true, a judgment of partial inclusion, at any rate, 
must be correct. The rule, then, that we should deduce from 
such an examination would be, " Either E or I must be true ;" 
this, when required for formal use, being converted into its 
equivalent categorical propositions, " The case of E being 
false, is a case of I being true ;" and '^the case of I being false. 



4:2 OF KEASONING OR ARGUMENT. 

is a case of E being true." Taking the example given above, 
we have for the complete syllogism, 

The case of E being false is a case of I being true, 
The present is a case of E ('^ no metals are vaporisable ") 
being false ; 

.*. The present is a case of I ('^ Some metals are vaporis- 
able ") being true. 

In logical language, when we assert the truth of any pro- 
position, we are said to ^osit it ; when we deny its truth, we 
remove it. Consequently the above rule is thus technically 
expressed, '' From the position of E we may infer the removal 
of I ; from the removal of E we may infer the position of I ; 
and, in both cases, vice versdj* The relation thus declared to 
subsist between E and I, is called contradictory-opposition, 
and E and I are termed the contradictories of each other. 

I have now I trust shown, once for all, that the inference 
which obtains in cases of opposition, is mediate, and may be 
regularly expressed in the syllogistic form. I shall, therefore, 
in recounting the remaining kinds of opposition, merely give 
the usual logical rules for the position and removal of propo- 
sitions, without discussing their bases, as the student will be 
able to do this for himself, by following the method of proce- 
dure adopted above.* 

There are four kinds of opposition : contradictory, contrary, 
subaltern, and subcontrary. 

Contradictor!/ opposition exists only between E and I, 
although those writers who do not recognise U and Y, describe 
it as also existing between A and 0. The rule of this oppo- 
sition is, *^ The position of a judgment infers the removal of its 
contradictory ; the removal of a judgment infers the position 
of its contradictor}^" It has been fully explained above. 

Contrary opposition exists between those pairs of judgments 
which may be false together, but cannot at the same time be 
true. These are A and E, A and U, A and O, A and Y, 
U and Y, U and 0, E and U, and E and Y. The rule is, 
*'The position of a judgment infers the removal of its con- 
trary." Nothing, however, follows from the removal of a 
judgment. Thus, " All whales are warm-blooded," and " Some 

* For further remarks upon this subject see Appendix B. 



SYLLOGISMS. 43 

whales are not warm-blooded," are contraries (A and 0) : if 
v/e admit the former, we must deny the latter, but if we 
deny the latter, we are in doubt whether to say, *' All whales 
are all the warm-blooded (things) " (U), or, " All whales are 
(some) warm-blooded " (A). 

Subaltern opposition exists between certain pairs of judg- 
ments which may be true or false together, viz., A and I, 
U and I, Y and I, E and 0, and Y and 0. In these cases, 
that judgment which has most distribution in its terms is 
called the sub alternant, its opposite being styled the subal- 
ternate. Thus I is subalternate to A, U, and Y, while is 
so to E and Y. The rule here is that, '^ The position of the 
subalternant infers the position of the subalternate." 

Subcontrarij opposition exists between I and 0, which may 
be true, but cannot be false together ; accordingly, the rule in 
this case is, '' The removal of a judgment infers the position 
of its subcontrary." Y and have been termed subcontraries 
by Dr. Thomson, but they would rather appear to come 
under the head of subaltern opposition, where it will be ob- 
served that I have placed them. 

It is proper to remark here that the word opposition does 
not in logical language imply an incongruiti/ of two judgments, 
for we have just seen that there are some cases where opposed 
propositions may both be true at the same time : it is merely 
a name given to a certain relation existing between the various 
forms of judgments, such relation differentiating as the forms 
themselves differentiate. Therefore, when Sir William 
Hamilton states* that '• there is no opposition between sub- 
contraries," and that to say so *' is a mistake," he appears to 
have been misled by grafting the ordinary sense of the word 
'' opposition " upon its logical signification ; for at a short 
distance previously we find him declaring opposition to be a 
relation existing between two judgments which are '* opposed 
or conjiictiver It is, however, somewhat strange that he 
should omit to take any notice of subaltern opposition as such, 
and content himself with merely mentioning it as a relation of 
subordination. He, it will thus be seen, admits of only two 
kinds of opposition — contradiction and contrariety. 

* " Lectures on Logic," vol. i. p. 261. 



44 OF REASONING OR ARGIDMENT. 

It is generally the practice in logical works to give a figure 
or " scheme " of opposition ; and, as this plan is useful in 
many respects, I subjoin the following, which shows at a 
glance the relations that have been described above as exist- 
ing between the various forms of propositions. 

(All X is all Y^ U Contrary -Y (Some X is all Y) 



%.^' 







(All X is some Y) A- — Subaltern 1 (Some X is some Y) 



(No X is Y) E— Subaltern (Some X is not Y) 






(All X is all Y) U Contrary Y (Some X is all Y) 

§ 4. Convei'sion, 

Conversion is the technical name applied to the operation of 
forming one judgment from another in such a manner that 
the subject and predicate of the original proposition (the cori' 
vertend) shall be respectively the predicate and subject of the 
new one (the converse). Thus, ^^ Some men of great imagina- 
tion are all the good poets," is said to be the converse of ** All 
good poets are men of great imagination." 

Now it is evident that a process of inference takes place 
here :* let us, therefore, inquire into its nature. 

The import of our first judgment is that the class of 
" good poets " is included, amongst other things, in the class 

* See Appendix B. 



SYLLOGISMS. 45 

of " men of great imagination ;" and as we know from the 
natural laws of extension that when one thing is included 
in another, a part of the object including is equal to the 
whole of the object included, — we therefore see that in the 
present case it will be allowable to predicate the entire class 
of good poets/' of '' some men of great imagination." Accord- 
ingly, we frame a general judgment which may be applicable 
to all cases, and which runs thus, " A case of A is the case of 
the same subject and predicate being reversed and thrown into 
the form of Y." 

The syllogism, then, will be as follows : — 

A case of A is a case of Y containing the same terms as 

A, but reversed in position, 
The present case (" all good poets," &c,) is a case of A ; 

.*. The present case is a case of '^ some men of great 
imagination are all good poets." 

The general practice, however, with regard to conversion is 
the same as that pursued in reference to opposition : instead 
of framing a syllogism every time we wish to convert a pro- 
position, we employ certain rules which enable us to perform 
the operation in a more speedy manner. These rules are : — 

1. The quality of the converse must be the same as that 

of the convertend. 

2. No terms must be distributed in the converse, but 

such as are distributed in the convertend. 
If the above rules be adhered to, no difficulty need be ex- 
perienced "in converting any proposition whatever ; but as a 
means of facilitating the process still more, the following table 
will be found useful. 

IT may be converted into U 

A * „ ,. .. Y 

E .. ., ., E 

Y ., .. .. A 

I „ ., ,. I 



O 
n 



V 

O 



One peculiarity of this table w^ill be at once noticed by the 
student : I allude to the employment of the form r]. This 
is necessitated by the consideration that if we follow the rules 



46 OF REASONING OR ARGUMENT. 

just given, we can only convert into rj ; it is, ho7v'ever, 
a conversion which is never likely to be made, for, as stated 
in a former part of this work (p. 34), is '* a much more 
forcible and convenient mode of expression " than ?;. 

The above method of conversion may be termed simple- 
conversion, although this name is usually limited to the con- 
version of E and I ; that of A being called conversion per 
accidens, or h]/ limitation, in consequence of a particular pro- 
position being educed from a universal ; while is treated as 
inconvertible.* 

There is another process which is sometimes considered as 
a species of conversion, and which may well be examined in 
the present place. It is variously termed conversion by 
equipollence, by contraposition, by negation,'\ by double nega^ 
tion,\ and immediate inference hy means of privative concep- 
tions ; § the name which I shall employ will be privative -con- 
'version, as this both indicates the nature of the process, and 
is harmoniously opposed to the term simple conversion. 

The modus operandi of privative -conversion consists in 
changing the quahty of the convertend, and altering its 
predicate into a corresponding positive or privative concep- 
tion, according as the case may be. The reasoning pro- 
cess which forms the foundation of the doctrine is as follows. 
Take some proposition in A, as, " All intellectual men are 
amiable," and let us think what it is that we know about its 
terms : the judgment itself makes us aware that '* intellectual 
men " are in the class of *^ amiable men," but gives us no 
further information regarding the latter class ; we know, how- 
ever,^ that it is possible to form a conception which shall in- 
clude every man not comprised under '^ amiable men," and 
that then we may deny the latter of the former : this we pro- 
ceed to do, and say, *^ No amiable men are unamiable " — a 
judgment which supplies us with the desired premiss, and 
enables us to form a complete syllogism ; thus : — 

* Here it will be seen that I allude to those writers who only admit 
A, E, I, and O. 
f Whately's '* Elements," Book ii. chap. ii. § 4. 
% Hamilton's " Logic," vol. ii. Appendix V. c. p. 267. 
§ Thomson's " Outlines," § 86. . U Supra, p. 20. 



SYLLOGISMS. 47 

No amiable men are iinamiable, 
All intellectual men are amiable ; 
.'. No intellectual men are unamiable. 
This conclusion is the converse required, and is seen to 
fulfil all the conditions of privative -conversion ; that is, its 
quality is changed, and its predicate is replaced by a cor- 
responding privative -conception. 

§ 5. Coincident Junction, 

When one class is said to be comprised in another we 
mean that all the members of the former are also members 
of the latter. Accordingly, these members may be considered 
as objects which {inter alia) are composed of two sets of ideas 
inseparably connected. We cannot, therefore, add anything to 
one idea and not at the same time add it to the other: nor for 
the same reason can we add one of the ideas to anything, with- 
out also adding the other. These considerations supply the 
general principles of what may be termed the doctrine o^ coin- 
cident -junction^ and which is thus expressed : ^' From any 
judgment we may form another by adding some marks equally 
to the subject and to the predicate ; or we may add the sub- 
ject and predicate as marks to some fresh conception." Thus 
if " a metal is a soKd " be true, we may also infer that '* a 
red metal is a red solid ;" or if we admit that '^ Logic is 
the science of the laws of thought," we must equally admit 
that " the study of Logic is the study of the science of the 
laws of thought." The former of these inferences has been 
termed ^* immediate inference by added determinants ;" the 
latter, ^^ immediate inference by complex conceptions." It will, 
however, be readily seen from the above investigation of the 
principles involved, that these reasonings may be exhibited in 
the syllogistic form, as easily as any of the others. 

This concludes the discussion of those arguments which are 
commonly styled immediate inferences; and, accordingly, 
whenever we have occasion to employ them in any future 
portion of this work, they will be considered as falling under 
their own special rules, and not as regular syllogisms. Such 
a course will be the more convenient as it will be more famihar 
to the student ; for the general laws which constitute the third 



48 OF REASONING OR ARGUMENT. 

propositions of such syllogisms as have been already con- 
sidered, are so firmly fixed in our minds, that we are scarcely 
conscious of their existence, until our attention is specially 
directed to them ; and, consequently, it may almost be said 
that they are never overtly employed in the eduction of so- 
called immediate inferences. 

It will of course be understood that these arguments are 
not limited to a single operation ; for it is possible to start 
with a judgment and successively employ the three processes 
of opposition, conversion, and coincident -junction, until we 
arrive at some other proposition which may satisfy our re- 
quirements. Such a proceeding is sometimes said to be merely 
a determination of a proposition's full signification ; but this 
may be said in effect of all reasoning whatever, for " an ex- 
tendon of any science through Logic is absolutely impos- 
sible ; as by conforming to logical canons we acquire no 
knowledge, receive nothing new, but are only enabled to 
render what is already obtained, more intelligible by analysis 
and arrangement." *" 

§ 6. Mediate Inference formally expressed as such, — Its 
Divisions, 

When an act of reasoning is fully expressed in words, i.e.^ 
if the three judgments be articulately stated, we have what is 
termed a syllogism. But as we saw, when treating upon pro- 
positions, that these are of three kinds, categorical, condi- 
tional, and disjunctive ; so in like manner are syllogisms 
divided, according as they contain these respectively. Thus 
the syllogism, " All A is B ; is A ; therefore is B," is cate- 
gorical ; '' If A is B, is D ; A is B ; therefore is D," is 
conditional ; and, '* Either A is B, or is D ; A is not B ; 
therefore is D," is disjunctive. 

Now the two latter species of syllogisms may always be re- 
duced to the former when occasion requires, and therefore an 
examination of the necessary laws of reasoning, together with 
the systematic arrangement induced by these laws, will best 
find place under the head of categorical syllogisms. Accord- 
ingly, in the following analysis, I shall speak simply of the 
* Hamilton's '* Logic," Lect. iii. p. 44. 



SYLLOGISMS. 49 

arguments so denominated ; this plan being consonant with 
that pursued when judgments were discussed. 

§ 7. The Fundamental Law of Mediate Ivferencc. 

*' Thought," says Sir W. Hamilton, " is the cognition of 
any mental object by another in w^hich it is considered as in- 
ckided ; in other words, thought is the knowledge of things 
under conceptions." This accords with what I have already 
stated concerning the grand principle of classification which 
underlies our faculties of acquiring knovviedge ; and prepares 
us to appreciate the fundamental law of mediate inference, 
which is as follows : — ^* Whatever belongs or does not belong to 
the containing ichole, belongs or does not belong to each and all 
of the contained parts."'^ This law, commonly called the 
" dictum de omni et nullo'' we owe to the commanding genius 
of Aristotle, who first placed Logic upon a sound and durable 
basis. It is not, however, to be understood that this dictum is 
directhj applicable to every case of reasoning ; the assertion 
merely being that the validity of any argument is idiimately 
referable thereto.^ 

For practical purposes men seldom ascend to general and 
fundamental truths, but devise a system of rules which, being 
immediately applicable, may obviate much of the inconvenience 
and delay that would otherwise ensue. Hence it is that logi- 
cians have developed Aristotle's dictum into the following 
proximate canon. " If two notions agree either wholly or in 
part with one and the same third, they agree with each other ; 
but if one of them is agreed and the other disagreed with the 
same third, they disagree with each other." This canon is, 
however, differentiated still further, thus : — 

1. A syllogism^ must cqntain three, and only three, terms, con- 
stituting three, and only three, iJropositions. The force of this 
rule is at once evident when we consider that the object sought 
to be attained by syllogising, is to determine the agreement 
or disagreement of two notions by respectively comparing 

* Hamilton's "Logic," Lecfc. xvii. p. 321. 

f Some objections having been raised by Mr. Mill and others to this 
account of the fundamental law of mediate inference, I have discussed the 
question at greater length in article C of the Appendix. 

D 



50 OF REASONING OR ARGUMENT. 

them with a third. This, of course, could not be done if we 
employed more or less than the three terms, or formed more 
or less than the three judgments. 

The names of these terms depend upon their position in the 
syllogism. The predicate of the conclusion is called the major 
term : the subject of the conclusion is called the minor term ; 
while the third notion with which the two former are each 
compared is styled the middle term. In like manner are 
the premises named, that in which the major term is com- 
pared with the middle being the major premiss ; the other, 
the minor premiss. 

Much objection has been taken to this employment of 
the words major and minor on account of their ordinary sig- 
nification being respectively " greater " and *' smaller," whereas 
it sometimes happens that the minor term is in reality greater 
than the major term, or that we are unable to compare them 
together as regards their extent. There is no doubt that 
these names were originally imposed from their representing 
the facts of the case in one particular form of syllogism which 
was considered the most perfect ; but as they have continued 
to be used by numerous logicians who were well aware of how 
the matter stood, it must be inferred that'' major" and "minor," 
when used logically, have merely a technical meaning as dis- 
tinguishing the terms of the conclusion, and not. as implying 
any relative degree of amplitude. A parallel case is to be 
found in the, use of the word *' opposition " (see, p. 41). In 
consequence of such objections, the premises of a syllogism 
have been variously re-named, the appellations oi proposition, 
lemma, and sumption^ being bestowed upon the major premiss, 
while the minor is known as the assumption^ suhsiimption, or 
lii/polemma. 

2. The premises must not both he negative. This follows 
from the consideration that a term can only show the relation 
of agreement or disagreement subsisting between two others, 
in so far as it is applicable to one of them at least. If, for in- 
stance, we were first to say, *'No mathematician is a good moral 
reasoner," and then that '* Shakspeare was not a mathema- 
tician," these statements would give us no grounds of com- 
parison between the notions of " Shakspeare " and " good 



SYLLOGISMS. 51 

moral reasoner." We should still be uncertain as to whetlier 
the latter might or might not be predicated of the former. 

3. If either of the premises he negative, the conclusion must also 
he negative^ for this is precisely the case stated in the second 
portion of the proximate canon above laid down, viz., "" If one 
notion is agreed and another disagreed with one and the same 
third, they disagree with each other.'* Thus, from the pre- 
mises, "no matter is imponderable," and *' all gases are matter," 
we can only conclude that ^' no gases are imponderable ;" for 
the attribute of imponderability was totally denied of matter, 
Vr'hich contains, inter alia, all gases. 

4. When the premises are affirmative, if either of them he 
attrihutive, the conclusion must also he attrihutive. Since a 
substitutive premiss implies a total identicality in extent of 
the middle term with one of the terms of the conclusion, 
and an attributive premiss implies only a partial identicality 
of Hke nature, it follows that between the terms of the con- 
clusion a partial identicality of extent is all that can be in- 
ferred. An example of this will be found in the following 
syllogism : — 

Compounds are all bodies which may be resolved into 

simpler forms (U), 
Sugar is a compound (A) ; 
.-. Sugar is a body which may be resolved into a simpler 

form (A). 

5. The middle term must he more than distrihxited in the 
p7^eniises, hoth taken together. For if this were not the case 
we should have no real inference whatever ; as witness this 
apparent syllogism — 

Some beautiful objects are pictures. 
Some hideous objects are pictures ; 
.*. Some hideous objects are beautiful. 
Here the two premises are in the form I, which we know 
does not distribute the predicate, this, in the present case, 
being the middle term '' pictures." Accordingly, the major and 
minor terms may, for anything the form of expression can tell 
us, be compared w^ith aifferent portions of the same thing ; 
and this, being equivalent to employing two middle terms, 
would violate the first rule, which prohibits the appearance of 

D 2 



52 OF REASONING OR ARGUMENT. 

more than three terms altogether. Of course it might so 
happen that when premises of the above nature were used, we 
arrived at a true conclusion, as in the following case : — 
Some beautiful objects are pictures, 
Some valuable objects are pictures ; 
.*. Some valuable objects are beautiful. 
This conclusion would, however, still be considered as invalid, 
that is, as not following directly and inevitably from the pre- 
mises ; for Logic, it will be remembered, regards not the matter, 
but merely the form of reasoning. 

Usually the middle term is distributed in one of the pre- 
mises at least; we can then tell at a glance that the rale 
now under discussion is not violated. Take, for example, the 
syllogism — 

All the metamorphic rocks have been subjected to the 

action of heat. 
Gneiss is a metamorphic rock ; 
.'. Gneiss has been subjected to the action of heat. 
The major premiss being A, distributes the middle term ; 
and as this must be again mentioned in the minor premiss, it 
will necessarily be more than distributed, and will not affect 
the validity of the conclusion. 

Sometimes, however, we meet with a syllogism whose pre- 
mises contain the middle term in such a manner as to show 
that the portions employed in each, if added together, would 
give more than the whole ; e.g. — 

Twenty per cent, of these knives are bad, 
Ninety per cent, of them are apparently well-made ; 
.'. Some of these apparently well-made knives are bad. 
In this case suppose that the notion " bad " coincides with 
the entire portion of ^' these knives," with which *' apparently 
well-made " does not ; such portion being only ten per cent, 
would still leave a further extent of ten per cent, to be ac- 
counted for, and this it is evident must come out of the 
*' ninety per cent. ;" so that we are sure that the notions 
'^ apparently well-made," and " bad," must correspond to 
the extent of ten per cent, at least : this is asserted in the 
conclusion. 

It will in this place be opportune to remark that much con- 



SYLLOGISMS. 53 

fusion frequently results from the use of an amhir/uous middle 
term, thus : — 

Capes are articles of clothing, 

Some tracts of land are capes ; 
.*. Some tracts of land are articles of clothing. 
This syllogism is logicallij correct, that is, in form ; but if 
we examine its matter, we shall see that it contains two middle 
terms, for in the major premiss one kind of "cape'* is spoken of, 
while in the minor, another kind is alluded to. The discussion 
of such cases will be further conducted when we come to 
examine the subject of fallacies. 

6. In the conclusion no term must he distrihufed, unless it 
has also heen distributed in one of the premises. The terms 
of the conclusion only agreeing or disagreeing with each other 
in so far as they respectively agree or disagree with the 
middle term ; they can merely be compared with each other 
by means of those portions which were found to coincide in 
any way with the middle term. 

All trees are organised beings (A), 

Men are not trees (E) ; 
.'. Men are not organised beings (E) ; 
And again — 

Diamonds are combustible (A), 

Some precious stones are diamonds (I) ; 
.'. All precious stones are combustible (A). 
In the former of these syllogisms we have an illicit process 
of the major ; that is, the major term is distributed in the con- 
clusion without being so in its premiss : in the latter there is, 
in like manner, an illicit process of the minor. The valid con- 
clusions which might be inferred would respectively be " men 
are not some organised beings " (r;), and '^ some precious stones 
are combustible " (I). 

By the six foregoing rules may all syllogisms be tested to 
ascertain whether they are real or only apparent, — whether the 
reasoning is correct, or incorrect. They are of great practical 
importance, as they enable us to dispense with the reduction 
of many syllogisms into a form where the dictum of Aristotle 
might be directhj applied ; but, as already stated, they must 
only be considered as proximate differentiations of one fun- 
damental truth. 



o4 



OF REASONING OR ARGUMENT. 



§ 8. 0/ Figure. 

In order to facilitate a full examination of syllogistic argu- 
ments, that is, of arguments formally expressed, logicians have 
investigated the number of positions which the middle term may 
assume in the premises, and in accordance thereto, have formed 
four classes, under which all possible syllogisms may be ranged. 
These classes they call figures, the form of which may be 
represented as follows ; employing P to signify the major term 
(predicate of conclusion), S the minor (subject of conclusion), 
and M the middle. 



1st Fig. 


2nd Fig. 


3rd Fig. 


4th Fig 


MP 


PM 


MP 


PM 


SM 


SM 


MS 


MS 


\SP 


.-. SP 


.-. SP 


.-. SP 



Thus when the middle term is the subject of the major 
premiss, and the predicate of the minor, we have the first 
figure ; when it is the predicate of both, the second ; when it 
is the subject of both, the third ; and finally, when it is the 
predicate of the major, and subject of the minor, there results 
a syllogism of the fourth figure. 



§ 9. Remarks upon the four Figures. 

1. The first figure is the most natural and obvious form, into 
which an act of reasoning can fall ; the cause of this apparently 
being that it is the only one in which the Aristotelian dictum 
will at once and immediately apply. Thus, to give a concrete 
example — 

The rushing of particles to a nucleus causes the body so 

formed to rotate. 
The earth was formed in this manner ; 
.*. The earth rotates. 

This argument, w^iich is employed by ^ the author of 
" Vestiges of Creation," I have expressed in popular language, 
but the student will find no difficulty in arranging it according 
to the model ;■ '' All M is P ; S is M ; therefore S is P." 

2. The second figure, though a somewhat distorted method 
of stating an argument, is yet very useful and ready in certain 



SYLLOGISMS. OO 

cases, where we desire to prove tbat some distinction exists 
between two notions, so as to prevent one of them inchiding 
the other. Suppose, for instance, we wished to prove that a 
certain substance did not contain the metai sodium ; we might 
employ such a syllogism as the following : — 

Any substance containing sodium would give, when 

burnt, two yellow bands in its spectrum (U), 
This substance when burnt does not do so ; 

.'. This substance does not contain sodium. 

Here the middle term forms the predicate of both premises ; 
consequently, the syllogism is of the second figure. If", how- 
ever, we wished to apply the Aristotehan dictum, it would be 
necessary to arrange this argument according to the first 
figure, such an operation being termed reduction. It consists 
in a skilful application of the doctrines of opposition, conver- 
sion, and coincident junction. In the present case all that 
we have to do is to substitute for the major premiss its simple 
converse, thus — 

Any substance which when burnt gives two yellow 

bands in its spectrum, contains sodium, 
This substance when burnt does not do so ; 

.*. This substance does not contain sodium ; — 
a syllogism most manifestly of the first figure. 

It has been held that in every case the mind unconsciously 
performs the process of reduction, and that therefore the 
second, third, and fourth figures are merely elliptical expres- 
sions of trains of reasoning, the first figure alone being an 
adequate representation of a single mediate inference. This 
statement, as implying a more direct influence than is usually 
imagined of the dictum npon our minds, is not unworthy of 
attention ; but since a full examination of the question would 
occupy more space than could be conveniently devoted to the 
purpose, I shall remain satisfied with having shown that any 
argument may be overtly expressed in such a manner as to 
evince its dependence upon the great fundamental law^ of 
reasoning. 

3. The third figure is of use when we wish to disprove a 
theory by instancing some example to the contrary. If we 
wished to combat the assertion that *' no bodies except water 



56 OF REASONING OR ARGUMENT. 

ever expand when cooling," we might do so in this manner : — 
Bismuth sometimes expands when cooling,* 
Bismuth is a body other than water ; 
.*. Some other body than water occasionally expands when 

cooling. 
The conclusion thus obtained is the contradictory (I) of 
the theory to be disproved (E), and accordingly our purpose 
is accomplished. In order to reduce this syllogism to the 
first figure, w^e must simply convert the minor premisa, when 
the whole will run thus — 

Bismuth sometimes expands when cooling, 
Some other body than water is bismuth ; 
.'. Some other body than water occasionally expands when 

cooling. 
4. The fourth figure is chiefly remarkable for the offence 
which it has given to many logicians, who accordingly have 
been neither sparing nor gentle in their attacks upon it : 
"tortuous," ''unnatural," "perverse," ''hybrid," "useless," 
" clumsy," " a monster," and " a caprice " may be taken as 
samples of the objections raised to its reception. It will, 
therefore, be advisable to examine the nature of some syllogism 
in this figure : take, for instance, De Quincey's-j- explanation 
of the non-existence of duelling among the ancient Greeks 
and Romans, which is as follows : — 

No duelling can exist wherever unlimited license of 

tongue is allowed to anger (E), 
Unlimited license of tongue was allowed to anger among 
the ancient Greeks and Romans (U) ; 
.'. Among the ancient Greeks and Romans duelling could 

not exist (E). 
Here it is objected that the mind naturally expects the 
converse of the conclusion, in accordance w^ith the tendency 
of the argument — this leading from "no duelling can exist 
where certain license is allowed," to " this license was allowed 
among the Greeks and Romans," and then in all symmetry 
to " no duelKng could exist among the Greeks and Romans." 
Now the answer to this is, that the figure of a syllogism 

* It invariably expands at the point of solidification. 
f Woriis. Author's Edition. Vol. vii. p. 281. 



SYLLOGISMS. ^ 57 

depending entirely upon the position of the middle term in 
the premises, it will not be affected by a change in the rela- 
tive positions of conclusion and premises. We have, therefore, 
only to state the conclusion first, and then give the premises 
as our reasons for forming it, when we shall at once obtain a 
smooth and naturally proceeding argument. Thus, we can 
say "' Among the ancient Greeks and Romans duelling could 
not exist ; for this is impossible where unlimited license of 
tongue is allowed to anger, which was the case in Greece 
and Rome ;" than which a more harmonious expression could 
not easily be found. 

In like manner, if we take mere arbitrary symbols to repre- 
sent the three terms, we shall still have a perfectly clear 
syllogism, e.g. — 

No S is P (conclusion) ; 
for No P is M (major premiss), 
and ]\r is all S (minor premiss) ; 
the meaning of which is, that none of the objects comprised 
by S are included by P, since the latter is totally excluded 
from ]\r, which contains the same objects as S. 

At the same time, however, that the fourth figure is thus 
shown to be perfectly legitimate and unforced, it may be 
readily conceded that it is but seldom used, as from the same 
premises and the converted conclusion we can form a syllo- 
gism of the first figure : thus, " M is all S ; no P is M ; 
therefore no P is S ;" which being, as it were, more familiar 
to the mind, is often er suggested. 

The formal reduction of syllogisms like the above to the first 
figure, is effected by simply converting both premises; e.g, — 
No M is P, 
All S is M ; 
.-. No S is P. 

§ 10. Of Mood or Mode. 

The arrangement of the propositions of a syllogism with 
reference to their quantity, quahty, and relation, is termed 
the mood or mode of the syllogism ; and as we are in posses- 
sion of symbols which fully express the form of a proposition, 
we can at all times represent the mood by the arrangement 

D 3 



OO REASONING OR ARGUMENT. 

of these letters : the conclusion, it is well to remark, being 
always placed last. 

Now as there are eight kinds of propositions, viz. U, A, 
E, Y], Y, I, 0, and w, — it follows that five hundred and twelve 
forms of syllogisms or moods may be made. Most of these, 
however, do not constitute valid arguments, and therefore we 
must reject them ; e.g, A A has an affirmative conclusion, 
though one of its premises is negative ; EGO has both ipre- 
TCiises negative ; III has either the middle undistributed or 
else an illicit process; and so on in numerous other cases. In 
like manner some moods are admissible in one figure, but 
not in another ; thus, A 1 1 is valid in each of the first and 
third figures, but in the second and fourth the middle term 
v^^ould be undistributed, 

§ 11. Table of Valid Syllogisms in each Figure, 
From the foregoing considerations it will be evident that 
a table may be constructed which will show all the valid syl- 
logisms falling under each figure ; and as such a table is of 
great practical use, I have drawn up the following : — 

Table of Modes. 



Fig 


. I. 


Fig. 


II. 


Fig. 


III. 


Fig. IV. 


Aff. 


Neg. 


Aff. 


Neg. 


Aff. 


Neg. 


Aff. Neg. 


AAA . 


EAE 


AUY . 


AEE 


AAI 


E AO 


AAI . AEE 


All . 


EIO 


AYY 


AOO 


All 


EIO 


AUA . E AO 


AU A . 


EUE 


. . , 


E AE 


AUA 


EUE 


AUY . EIO 


A YI . 


EYO 


• 


EIO 
EUE 
EYO 


AYA 


EYE 


. . .EUE 
. . .EYE 
. . .EYO 


lUI . 


OUO 


lUI . 


. 


I AI 


\ OAO 


I AI 


I YI . 


OYO 


I YI . 




lUI 


OUO 


lUI 


U AA . 


UEE 


UA A . 


UEE 


UAY 


. UEE 


UAY .UEE 


UII . 


UOO 


UII 


UOO 


UII 




UII .UOO 


UUU . 


, 


UUU . 


. 


UUU 


, . 


UUU 


UYY . 


• • • 


UYY . 


• • 


U YA 


. . . 


UYA 
UYY 


YUY . 


YEE 


YAA . 




YAY 


. YEE 


YII 


YY Y , 


YOO 


YII . 

YUA 

YYI 


• 


YUY 




YUA 
YYI 



SYLLOGISMS. 60 

The above table is arranged alphabetically, so as to facili- 
tate reference, and enables us at once to determine the 
validity or invalidity of any syllogism whose figure is known ; 
for if legitimate, it will be found in its proper position, while 
if inadmissible, it will be absent. 

The propositions 17 and w have been omitted from this 
table on account of their small importance (see p. 34). It 
may also be proper to remind the student that in most of the 
older treatises on Logic he will find tables of judgments which 
differ materially from the one above given, inasmuch as they 
only recognise the four propositions A, E, I, and 0. The 
usual form in which such a table is given consists of the 
following four mnemonic Latin verses : — 

Fig. I. Barbara, Celarent, Darii, Ferioque, prioris ; 

Fig. II. Cesare, Camestres, Festino, Baroko, secundce ; 

Fig. III. Tertia, Darapti, Disamis, Datisi, Felapton, Bo- 
kardo, Feriso habet : quarta insuper addit 

Fig. IV. Bramantip, Camenes, Dimaris, Fesapo, Fresison. 

These lines, or rather the first three, were the invention of 
Pope John XXII. , whose work upon Logic, under his name 
of Petrus Hispanus, enjoyed great celebrity. To each of the 
four figures it will be observed that a verse is appropriated, 
consisting chiefly of a number of names distinguished by 
capital letters,* and containing three vowels ; the vowels .thus 
employed serve to indicate the mood of the respective syllo- 
gisms. For instance, the syllogism '^ all M is P; all S is M ; 
therefore all S is P," is said to be in the mood barhara, 
which signifies A A A in Fig. I. The consonants of the 
various moods are intended to assist the process of reduction ; 
the initial letters show that each mood must be reduced to 
that mood in the first figure which is similarly characterised : 
s indicates that the proposition immediately preceding is to 
be simply converted (in its old acceptation ; see p. 46) ; p 
that it is to be converted per accidens, except in the mood 
hramantip, where it denotes that the conclusion (I) will, when 
the syllogism is reduced, become A ; m that the premises are 
to be transposed ; and k that the contradictory of the con- 

* Tertia, in the third verse, is merely employed for the sense of the 
expression, and is not a mood. 



60 OF REASONING OR ARGUMENT. 

elusion is to be substituted for the immediately preceding 
proposition. The two moods, however, in which h ©ccurs 
(baroko and hokarko) may be more simply reduced by em- 
ploying the process of privative conversion ; they will then 
become ferio and darii respectively. 

An example will perhaps assist in rendering the above 
description intelligible. Let us take a syllogism in disamis ; 
thus, — 

Some rocks have been formed by the action of water (I), 
All rocks are solid (A) ; 
.'. Some solid things have been formed by the action of 

water (I). 
Here the m indicates that the premises must be transposed, 
the major and conclusion being simply converted in accordance 
with the requirements of s and s. When this is done, we 
obtain the following : — 

All rocks are solid (A), 

Some things which have been formed by the action of 
water are rocks (I) ; 
.*. Some things which have been formed by the action of 
water are solid (I) ; — 
which is a syllogism in darii, that mood of the first figure 
which was indicated by D, the initial letter of disamis, 

I have thought it advisable to enter at some little length 
upon this subject, as these ancient names of moods are not 
confined to logical works, but are often to be met with in old 
authors ; in addition to which, it might be expected that in a 
work like the present, of professedly a practical character, 
some notice would be taken of a method so universally fol- 
low^ed. In fact, the perfect adaptation of the above quoted 
lines to their purpose, would alone render them deserving of 
mention; for, as Sir William Hamilton observes, " it must be 
confessed that, taking these verses on their own ground, 
there are few human inventions which display a higher 
ingenuity." 

It must also be observed that so far from the method just 
described being out of date and obsolete, it may still be 
applied in many cases ; the only difference between it and 
the table of judgments given in the present volume, being 



SYLLOGISMS. 61 

that the latter is much more complete, containing not only 
all that the A, E, I and system includes, but many other 
syllogisms in addition. 

§ 12. Induction and Deduction, 

We have now seen that all acts of mediate inference when 
formally expressed, ^.e. all syllogisms, may be systematically 
arranged and discussed under the two heads of mood and 
figure. There are, however, some further divisions of syllo- 
gisms which require our attention ; the first of these being 
that into inductive and deductive. 

The distinction between these two methods of reasoning 
may be thus expressed : induction is the process of forming 
a general law ; deduction, that of applying a law so made to 
some particular case or cases. Or, in other words, induction 
consists in reasoning from the parts to the whole ; deduction, 
in reasoning from the ichole to the parts. In formal Logic, 
however, this distinction is comparatively unimportant, as 
vvill be seen from the following considerations. 

Take some inductive syllogism, as follows : — 
Oxygen, chlorine, and steam are elastic (A), 
Oxygen, chlorine, and steam are all gases (U) ; 

.". All gases are elastic (A). 

Here we see that from predicati;ig ''elastic" of the various 
parts '' oxygen, chlorine, and steam," we are enabled to pre- 
dicate it also of the whole thus constituted, viz., " gases.*' It 
is, therefore, evident that the general law or truth upon which 
the validity of such a syllogism depends, may be thus ex- 
pressed : — '' That which belongs, or does not belong, to each 
and every one of the parts, also belongs, or does not belong, 
to the whole." This law^ has been declared to differ from the 
dictum de omni et nulla, which, the student will remember, is 
to the following effect : '* That which belongs, or does not be- 
long, to the whole, also belongs, or does not belong, to each 
and every one of the parts." Now if we admit the difference 
thus asserted — that is to say, if we admit that these two laws 
are •' ecjually necessary and indejoendent " * — then we must, in 

* Hamilton's '• Logic," vol. i. p. 321. The italics are my own. 



62 OF REASONING OR ARGUMENT. 

addition, admit that the division into inductive and deductive 
syllogisms is imperatively called for, since each species of 
reasoning will have been shown to rest upon separate funda- 
mental* laws. 

That this independence, however, does not exist, may be 
shown by a few reflections based upon the nature of what we 
understand by the notion of a '* whole." In the case under 
examination the ** whole " of which we speak is the conception 
" gas.'* This, as the student will recollect from what was 
said in a previous chapter, is the result of our comparing 
various bodies together, and ascertaining those attributes in 
which they are all agreed ; the set of attributes so obtained 
being then abstracted to form the idea, and receive the name 
of '* gas»." Consequently, when we say '^ gases,'* we think of a 
class whose members are, not various individual objects, but 
various similar sets of attributes existing in separate bodies or 
objects, viz., "oxygen, chlorine, and steam;'* and when we 
say that what may be predicated of the class " gases," may also 
be predicated of each of its members, we mean that the attri- 
bute " elasticity," for instance, may be predicated of oxygen, 
chlorine, and steam, not -as individual objects, but as separate 
and similar sets of attributes ; or, in other words, we imply 
that each set of attributes must be capable of forming the 
idea "gas** in our mind«, and must, consequently, be of 
similar constitution with the remainder. In like manner, 
when we say that whatever may be predicated of each member 
may be predicated of the class " gases,'* we mean that what- 
ever attribute is common to oxygen, chlorine, and steam must 
form part of that set of attributes which is called " gas ;" that 
is, we imply that oxygen, chlorine, and steam, considered as 
definite sets of attributes, are of similar constitution, and must 
consequently each be capable of forming the same idea, " gas,'* 
in our minds. Now these two expressions, which are thus 
seen to have almost identical meanings, are the self-same 
laws which have been spoken of as independent of each other; 
this statement, therefore, is seen to be incorrect, and, accord- 

* As regards the use of the word fundamental in this place, see 
Appendix C. 



SYLLOGISMS. 63 

ingly, we need not consider the distinction between tlie pro- 
cesses of induction and deduction as more than a logical 
trifle. 

It must here be rigidly borne in mind, that the above 
remarks only apply to induction and deduction when con- 
sidered as divisions oi pure Logic ; for when we come to treat 
upon applied Logic, it will be found that another kind of 
induction exists, which necessitates a particular mention, and 
which is of very great importance. The difference between 
these two kinds of induction is closely connected with a fact 
which the student has doubtless observed, viz., that the minor 
premiss of our inductive syllogism is obviously incorrect, for 
so far from oxygen, chlorine, and steam being all gases, they 
only constitute an exceedingly small portion of the class. 
This brings us to the consideration that in formal Logic we 
have nothing at all to do with truth or falsehood ; we can only 
ascertain whether a conclusion legitimately follows from pre- 
mises already granted. Accordingly, we merely look upon 
the minor premiss with reference to its /arm, i.e., its quantity, 
quality, and relation, and not as regarding its matter, viz., 
the reality and nature of the notions composing the subject 
and predicate : thus, for all purely logical purposes, the pro- 
position might be replaced by " X, Y, and Z, are all S " 
without in the least interfering with the reasoning process. 
Applied Logic, on the contrary, takes into account the relative 
natures of the objects furnishing notions, and would construct 
the syllogism in the following manner : — 

Oxygen, chlorine, and steam are elastic (A), 
Oxygen, chlorine, and steam are gases (A) ; 

.*. All gases are elastic (A). 

Here it will be seen that the minor premiss is indeed true, 
but then there is an illicit process of the minor term, so that 
the syllogism cannot be admitted b.s formally valid. 

The deductive syllogism corresponding to our inductivo 
example would be as follows : — 

All gases are elastic, 
Oxygen is a gas ; 
.'. Oxygen is elastic — 
where the general law is applied to a particular case. 



64 OF REASONING OR ARGUMENT. 

§ 13. Extension and Intension, 

In a former chapter it was explained that a proposition 
might have its meaning regarded from different points of 
view, according as the subject and predicate were regarded 
intensively or extensively. Thus, when we say, '^ All fluids 
are compressible," we mean not only that the attributes of 
" compressibility " are among the attributes of every " fluid " 
(intension), but, also, that the class of " compressible sub- 
stances " numbers in its ranks all " fluids " (extension). This 
differentiation of meaning, in like manner, finds place among 
arguments, and thence has arisen a distinction of syllogisms 
into extensive and compreliensive (intensive). An extensive 
syllogism is of this nature — 

Motion is immaterial, 
Heat is motion ; 
.'. Heat is immaterial, — 
and would be thus interpreted : — 

Motions are contained in the class of immaterial objects, 
Heat is contained in the class of motions ; 
.*. Heat is contained in the class of immaterial objects. 
The same syllogism, if stated comprehensively, or inten- 
sively, would run as follows : — 

Heat is motion, 
Motion is immaterial ; 
.'. Heat is immaterial ; — 
and its meaning, when broadly stated, would be this : — 
Heat comprehends in it the attributes of motion. 
Motion comprehends among its attributes those of im- 
materiality ; 
.*. Heat comprehends the attributes of immateriality. 
An examination of these four syllogisms will reveal their 
dependence upon each other ; all of them being evidently the 
same result of the same process of reasoning. This is rendered 
clear by a brief analysis of the import which attaches to pre- 
dication. We say, for instance, that ** motion is immaterial," 
and in doing so we state that a certain relation of congruity 
exists between two compound ideas : " motion^'' which con- 
sists of two sets of attributes, viz., the generic feature *' imma- 
teriality * and certain specific differences ; and '' immaterial 



SYLLOGISMS. 66 

objects y' which like\Yise is duplicate, containing the notion 
" immateriahty " per se, and the notion of '^ immateriality " 
indefinitely repeated, as existing in combination with various 
sets of specific differences. It therefore results that the rela- 
tion implied by our predication is also compounded, its con- 
stituents being, that motion is an immateriahty united with 
certain distinguishing marks ; and that motion is capable of 
producing on the mind, together with other impressions, the 
same idea that immateriality per se would do. These two 
relations it will easily be seen are those of extension and 
intension. But another fact remains to be noticed : that 
although the two ideas and relations are thus shown to be 
compound, yet the union of their respective parts is so inti- 
mate that they cannot be separated. \Ye are unable to 
resolve the idea '' motion " into its two sets of attributes, 
'' immateriality " and " specific differences," so as to think of 
these separately, and at different times : we are also unable 
to divide the idea " immaterial objects " into " immateriality " 
per se, and *^ immaterialities " respectively combined with 
distinguishing attributes ; and, finally, we are unable to think 
of one of the relations above described without also thinking 
of the other. The utmost we can do is to bring one portion 
of the compound idea, or relation, into greater prominence 
than its fellow, by concentrating our attention as much as pos- 
sible upon the chosen part ; it being remembered that we can- 
not so concentrate the whole of our attention, and, therefore, 
we must always, in some measure, be impressed by the less 
important constituent. 

These observations, if taken in conjunction with those con- 
tained in the section upon induction and deduction, will, it is 
hoped, afford an intelligible and clear view of the manner in 
which the mind acts when comparing notions and judgments ; 
and as the operation is always identical, being, though com- 
plex, yet irresoluble, it follows that the only useful, or, strictly 
speaking, admissible division of judgments and reasonings, 
is that which merely refers to their form. Hence, in formal 
Logic the distinction between the processes of extension and 
comprehension must, like that between induction and deduc- 
tion, be considered as of trifling consequence. 



6Q OF REASONING OR ARGUMENT. 

§ 14. Denomination, 

When speaking of the interpretation of the copula, I men- 
tioned that another mode of doing so had been suggested, in 
addition to those connected with the doctrines of extension 
and intension. This was the interpretation of denomination, 
and is as applicable to arguments as to propositions : for ex- 
ample, the syllogism — 

All planets are stars, 
Mercury is a planet ; 
.*. Mercury is a star, 
may be thus translated : — 

Planets may be called stars, 
Mercury is a planet ; 
.*. Mercury may be called a star. 
This interpretation is, of course, merely verbally significant, 
and is not intended to imply any approach to a radical, or 
even formal difference between the syllogisms. The doctrine, 
if doctrine it may be called, must, therefore, be received as 
nothing more than a practical hint for turning a syllogism to 
some special account, and as such belongs properly to applied 
Logic. Former usage, however, is my excuse for placing it 
here. 

§ 15. Syllogistic Arrangement of Propositions, 

Before concluding the subject of pure-categorical syllo- 
gisms, it will be advisable to mention a matter about which 
the student might otherwise entertain an erroneous opinion. 
I allude to the oi^der of the three propositions constituting a 
syllogism. It will have been observed that the usual course 
pursued is to place the major premiss first, the minor next, 
and the conclusion last ; and it may consequently be thought 
that this order is the one most in accordance with natural 
laws. Such, however, is not the case ; the arrangement in 
question being merely an arbitrary practice adopted by 
logicians in order to facilitate their expositions of the science. 

In fact, it frequently happens that the conclusion occurs 
to. the mind as a problem or thesis, which requires certain 
judgments (premises) to be formed, in order that its validity 



SYLLOGISMS. 67 

may be apparent. Thus, I might suspect a certain gas to 
be hydrochloric acid, but in order to be sure it would be 
necessary for me to find some "proof of this. Accordingly, 
knowing the general law that ammonia produces white fumes 
only when brought into contact with hydrochloric acid, I 
should proceed to test the suspected gas in this manner ; and, 
the anticipated result following, I should be enabled to con- 
struct the syllogism : — 

This gas is hydrochloric acid ; 
Because, It produces white fumes with ammonia, 
And, Everything which does that must be hydro-^ 
chloric acid. 
Hero the premises and conclusion are reversed. Again, 
some fact comes under our notice, such as, " This metal takes 
fire upon touching water ;" we make inquiries, and find that 
'^ The only metal behaving in such a manner is potassium ;" 
hence we draw the conclusion that ** This metal is potassium." 
An argument so expressed is a syllogism of the first figure, 
but with the premises reversed. Accordingly, it thus appears 
that there is no natural and definite order of judgments ; it 
cannot, therefore, be said that any arrangement is incorrect, 
or alone correct, the disputes between logicians upholding 
different models being so many lost words, we can scarcely 
say arguments. 

§ 16. Conditional Syllogisms. 

We have now to consider the case of syllogisms whcse con- 
stituent propositions are not all pure-categoricals ; and first 
we wall 'examine those in which one or more conditional^ 
judgments appear, the argument being then termed a con- 
ditional syllogism. 

Now these reasonings may be treated in two ways — prac- 
tically, and theoretically; that is to say, their own special 
canons or proximate rules may be applied to them as they 
stand ; or they may be reduced to categorical syllogisms, 
when, of course, they immediately fall under the laws which 

* I omit modal propositions, as these cannot be treated otherwise than 
as pure-categoricals. See p. 28. 



G8 OF REASONING OR ARGUMENT. 

have been analysed in the foregoing pages. And, first, as 
they stand. 

Every conditional proposition consists of two parts — the 
antecedent and the consequent — -between which a certain rela- 
tion is asserted to exist. These parts are both distinct judg- 
ments, the relation being that the consequent depends upon the 
antecedent in such a manner as to necessitate the inference of 
the former if the latter be granted ; e.g,, " If the anchor holds 
out, the ship will be saved," where ** If the anchor holds out '* 
is the antecedent, ^' the ship will be saved" is the consequent, 
and the relation asserted is, that if we admit that the anchor 
will hold out, then we must also admit that the ship will be 
saved. A complete syllogism having such a proposition for 
a premiss, would be of the following form : — 

If the anchor will hold out, the ship will be saved, 
The anchor will hold out ; 

.*. The ship will be saved. 

In cases where hoth the premises are conditional, then the 
conclusion must be conditional also, e.g. — 

If the anchor will hold out, the ship will be saved, 

If the storm does not increase, the anchor will hold out ; 

.*. If the storm does not increase, the ship will be saved. 

Now, from a consideration of the relation subsisting between 
the antecedent and consequent of a conditional proposition, 
logicians have devised two practical rules, w^hich suffice to 
determine the validity of any conditional syllogism wdthout 
reducing it to a categorical form. These are : — 

1"^. If the antecedent he granted, the consequent may he in- 
ferred ; for this is merely to state the nature of the assertion 
made by the form of the proposition. Nothing, however, 
follows from granting the consequent : thus, in the proposi- 
tion '^ If he is truly wise, he will be happy," we must infer 
that he w^ill be happy, if we admit that he is truly wise ; but 
admitting him to be happy will not prove him to be wise, as 
it is possible for an ignorant person to enjoy himself. 

2^. If the consequent he denied, the antecedent may also he 
denied. This follows from the consideration that the truth 
of the consequent is necessitated by that of the antecedent, 
so that if the latter were true, the former would be so too. 



SYLLOGISMS. 69 

If, for example, we deny the consequent of this proposition, 
'' If he be shot through the heart, he is dead," and say that 
he is not dead, we may evidently infer that he is not shot 
through the heart; but to deny the antecedent would not 
enable us to say that he is not dead, because he may have 
been killed by many other causes. 

These two laws have given occasion to a division of con- 
ditional syllogisms into two moods, viz., the ponent, wherein 
the antecedent is granted, and the tollent, where the conse- 
quent is denied. These moods are reciprocally convertible, 
as may be seen from the following example : — 

If the moon is not shining, the night is dark, 
The moon is not shining ; 
.'. The night is dark. 

This is in the ponent mood ; but if we wish to make it 
tollent, we may do so by reversing the hypothetical, and duly 
negating, thus : — 

If the night is not dark, the moon is shining. 
The moon is not shining ; 
.*. The night is dark. 

These moods are also termed constructive and destructive, 
answering respectively to ponent and tollent. 

The second method of treating conditional-syllogisms is, 
by reducing them to categoricals. Such a proceeding has, 
indeed, been condemned by high authority* on the ground 
of its being unnecessary and not always possible. I venture, 
however, in common with many logicians,*!" to think that this 
condemnation is erroneous, as both of the objections urged 
may be thus disposed of. The reduction is necessanj, as, by 
this means, conditional-reasoning being brought under the 
same proximate laws with categorical arguments, is shown to 
be of exactly the same nature, and so the unity of the reasoning 
process is maintained ; at the same time, however, I do not 
contend that it is necessary iox practical purposes, as then the 
rules above explained would become inept. Again, that the 

* Krug's " Logik," p. 258. Bachmann's " Logik," § 89, Anm. 2. 
Sir W. Hamilton's " Logic," vol. i. p. 842. 

t Esser's " Logik," § 99; Wolfs " Philos. Rat./' § 412; Whately's 
" Elements," book ii. chap, iv., \ 6 ; Thomson's '* Outlines,'* § 73. 



70 OF REASONING OR ARGUMENT. 

reduction is never impossible, may be seen from the very case 
adduced as presenting insuperable difficulties, viz., '' If A is 
C, B is D ; but A is ; therefore, B is D ;" where we have 
only to say, ^^The case of A being C is a case ofB being D ; 
the present case is a case of A being C j therefore, ^7^e present 
case is a case of B being D," and 'the obstacle is surmounted, 
the resulting syllogism being a categorical in A A A, Fig. I,, 
or, as the old logicians would say, in Barbara. The re- 
spective te7^ms are here distinguished by being printed in 
italics. 

That these objections should have been brought against 
the reducing process as applied to conditional syllogisms, is 
apparently owing, first, to the acceptance of the principle, 
*^ Infer nothing without a ground or reason " as a necessary 
and primary law of thought ; and, secondly, to its being lost 
sight of that a term may be composed of more than one 
conception. With regard to the first of these causes, it may 
be observed, that the law there mentioned, called the law of 
reason and consequent, has been a subject of much discussion 
among metaphysicians and logicians, but should properly be 
referred to the former alone. By it the antecedent is ex- 
plained as being ^* the complement of all, without which 
something else would not be," and the consequent as being 
*' the complement of all that is determined to be by the 
existence of something else." This, which is Sir William 
Hamilton's explication, given with especial reference to con- 
ditional propositions, is, however, too w^ide and general for 
application in such cases ; since, were we to admit that the 
consequent ^' could not be " without the antecedent, we must 
also admit, that by denying the antecedent we may deny 
the consequent, w^iich is contrary to the second rule above 
given. It is likewise too wide and general to be considered 
as a separate law, for if the antecedent be the " complement 
of all, without which something else would not be," it must 
necessarily be that "something else" itself. Now, a thing 
cannot be something else ; and, therefore, in order to attach 
any admissible meaning to the definition under question, we 
must interpret it thus : — " The antecedent is the same thing as 
the consequent, but from a different point of view," a state- 



SYLLOGISMS. 71 

ment much the same as *^ a thing is itself," and answering 
to another primary law, viz., " whatever is, is." * Indeed, 
Sir William Hamilton's latest views wordd appear to have 
been in accordance with those advocated here, as we find 
him saying, that the law of reason and consequent ** should 
be excluded from logic." f 

The second source of objection which led to the statement 
that some conditionals could not be reduced, probably arose, 
as stated above, from an incomplete view of the structure of 
terms. Thus, in the syllogism, '* If A is B, C is D ; but A 
is B ; therefore, is D ;" it was hastily concluded that there 
are four terms. A, B, C, and D ; but, in so doing, it is as- 
sumed that the reasoning process concerns these simple 
notions ; whereas, in fact, it is occupied with the more com- 
plex ideas, " A is B " and " C is D." Accordingly, instead 
of four terms, which of course would be incompatible with a 
categorical syllogism, we have only two, and require a third, 
viz., *^ the present case," before we can draw a conclusion. 
This third term is implied in the second premiss, when we 
say ''A ts B." 

During the course of the preceding remarks, the student 
will doubtless have observed the technical method of reduc- 
tion employed in these cases. It may be articulately enounced 
as follows : " Each conditional proposition is to be considered 
as a universal-affirmative -attributive categorical, with the 
antecedent for a subject, and the consequent for a predicate." 
Thus, the syllogism here stated,— 

If a body is struck, heat is generated. 

But if a meteorite falls into the sun, a body is struck ; 

.'. If a meteorite fails into the sun, heat is generated, 
may be reduced in the following manner : — 

All cases of " a body is struck," are cases of " heat is 

generated" (A), 
All cases of '^ a meteorite falls into the Gun," are cases 
of " a body is struck " (A) ; 

. . All cases of " a meteorite falls into the sun," are cases 
of " heat is generated." 

* As regards the primary laws of thought, see Appendix C. 
t ♦' Discussions," p. 603. 



72 OF REASONING OR ARGUMENT. 

In tliis way, or by using equivalent expressions, any condi- 
tional syllogism may be thrown into the form best adapted 
for displaying its real import a8 an act of reasoning. 

§ 17. Disjunctive Syllogisms. 

A disjunctive syllogism is an argument in which there is 
one, or more than one, disjunctive proposition, and may be 
represented by these formulae : P. ^' A is either C or D ; B 
is neither nor D ; therefore, B is not A." 2°. "A must be 
either C or D ; but it is not ; therefore, it is D." 3°. '^A is 
either 0, D, or E ; but it is not C ; therefore, A is either D 
or E." 4''. '' Either A is B, or C is D ; but A is not B ; 
therefore, is D," &c. &c. 

The import of the disjunctive propositions in all these syl- 
logisms is, that the cases enumerated are the only possible 
ones, and that they are mutually exclusive ; a perfect logical 
division has in fact been performed. Accordingly, the prac- 
tical rules which result are — 

1°. From the assertion of one alternative, we may deny all 
the others ; e.g., if in the proposition, " All men must be 
either white, black, red, or yellow," we were to affirm, " These 
men are red," we might infer that '' they are neither white, 
black, nor yellow." 

2°. From the disjunctive assertion of more alternatives than 
one, we may deny the rest. Thus, in the above example, if we 
were to say, for our second premiss, that '^ these men are 
either white or black," we should then conclude that " they 
are neither red nor yellow." 

3°. From the denial of one, or more than one alternative, we 
may assert such as remain ; directly, if one, disjunctively, if 
more. Accordingly, the following syllogism would be 
valid : — 

All poems are either epic, lyrical, or didactic. 
The poem of Paradise Lost is neither lyrical nor 
dadactic ; 

.'. Paradise Lost is an epic. 

The reduction of disjunctive syllogisms to categoricals is 
similar to that of conditionals. Take, for instance, the syllogism 
just quoted — it will become : — 



SYLLOGISMS. 73 

Poems which are neither lyrical nor didactic, are epics, 
Paradise Lost is a poem which is neither lyrical nor 
didactic ; 
.'. Paradise Lost is an epic. 

And here it must be stated, that in order to have a true 
conditional or disjunctive syllogism, it is necessary that the 
reasoning should hinge upon the consequence in the one case, 
and on the alternative in the other ; for it is possible for a 
conditional or disjunctive loroposition to exist in a categorical 
syllogism; thus. 

All simple forms of matter are indestructible as such, 
If the caloric theory be correct, heat is a simple form of 
matter ; 
.*. If the caloric theory be correct, heat is indestructible as 

such. 
In this case, ** If the caloric theori/ he correct, heat " must 
be considered as the minor term, for it is evident that the 
reasoning is merely a comparison of this, and the major term 
*' indestructible as such," with the middle " simple forms of 
matter ;" leaving the consequence of the conditional proposi- 
tion altogether untouched. 

§ 18. The Dilemma. 

If in a syllogism there be a conditional premiss, whose ante- 
cedent or consequent is composed of a disjunctive proposi- 
tion, such an argument is termed a dilemma, or hypothetico- 
disjunctive syllogism. Take, for example, the following : — 
If the army were defeated, it must either have sur- 
rendered or retreated, 
But it did neither of these ; 

.*. It w^as not defeated. 

The rules upon Avhich the validity of such syllogisms 
depend, are compounded of those referring to both condi- 
tionals and disjunctives ; thus, 1^. The antecedent heing 
affirmed, either disjunctively or not, as the case may he, the con- 
seque/it is also admitted j and 2°. The consequent heing denied, 
either disjunctively or not, as the case may he, the antecedent is 
also denied. 

An argument of the above description is termed a dilemma 

E 



i± OF REASONING OR ARGUMENT. 

ill consequence of its having two disjunctive members in the 
consequent of the major premiss : that is to say, it contains 
a double lemma, or double supposition. If there are three 
such members, it is a trilemma ; if four, a tetralemma, and 
so on ; but the name polylemma is usually applied to those 
containing more than four. Any one of these would, how- 
ever, be loosely called a dilemma. 

Such is the account commonly given of those arguments 
to which the name of dilemma is applied ; but it is incom- 
plete, as it does not refer to a class of syllogisms which, if 
anything, would fall more properly under that denomination. 
I allude to those in which several antecedents and consequents 
are disjunctively affirmed or denied ; e.g, — 

If he leaps out of the window, he wall severely injure 
himself; if he does not do so, he will be burned, 
But he must do either the one or the other ; 
/. He must either severely injure himself, or be burned. 
Or again — 

If this man were happy, he would not be angry ; and 
if he retained his self-command, he w^ould not be 
excited, 
But he is either angry or excited ; 
.*. He is either unhappy, or has lost his self-command. 
In these syllogisms, we see that the major premiss (so to 
speak) is composed of two distinct conditional propositions, 
thus being a truer di-lemma than the cases previously con- 
sidered. 

All hypothetico-disjunctive arguments may be reduced, 
either to conditionals or categoricals at pleasure. There is 
no difficulty in the process, it being merely a judicious com- 
bination of the methods already studied, and as a general 
model, the following formula will be all that is needed. It 
shows the categorical reduction of a complex-dilemma, that 
is, where the major premiss is composed of two distinct 
conditionals. 
Syllogism : — 

If A is, B is ; and if C is, D is, 
But either A is, or is ; 
.*. Either B is, or D is. 



SYLLOGISMS. lO 

Reduction : — 

1°. Take for a major premiss the categorical equivalent of 
the given minor ; and for a minor term, the denial of the 
consequent in the first conditional of the given major premiss : 
complete the syllogism, thus 

All non-A's are C's, 
All non-B's are non-A's ; 
.*. All non-B's are C's. 
2~. Take for a major premiss, the categorical equivalent of 
the second cpnditional in the given major ; and for a minor 
premiss, the conclusion of the syllogism last formed : the 
conclusion resulting from these premises, will be the cate- 
gorical equivalent of the disjunctive conclusion in the syl- 
logism given for conversion : e.g — 
All C's are D's, 
All non-B's are C's ; 
.*. All non-B's are D's ; 
or 
Either B is, or D is. 

§ 19. Incomplete Syllogisms. 

When any one of the propositions forming a syllogism is 
not overtly enounced, such an argument is termed an Entlii/- 
meme. It will be evident that there is no difference in the 
reasoning process between enthymemes and formal syllogisms, 
as the premises and conclusion are in both cases the same : 
the distinction merely consists in the number of judgments 
that may be actually expressed in words. Accordingly, 
since there are three propositions in every syllogism, enthy- 
memes are divided into three orders, which respectively 
suppress the major premiss, the minor premiss, and the con- 
clusion. Examples of them may be thus given : — 
The formal syllogism : — 

All women are inquisitive, 
Jidia is a woman ; 
.'. Julia is inqusitive. 
Enthymeme of the first order (the major suppressed) : — 
Julia is a woman ; 
/. Julia is inquisitive. 
e2 



7b OF REASONING OR ARGUMENT. 

Enthymeme of the second order (the minor suppressed) : — 

All women are inquisitive ; 
/. Julia is inquisitive. 
Enthymeme of ihe third order (the conclusion suppressed): — 

All women are inquisitive, 

And Julia is a woman. 
Into one or other of these three forms, nearly all argu- 
ments, as popularly expressed, fall ; for it is seldom that a 
person takes the trouble to state a syllogism in full. This 
elliptical method of overt inference, is most strikingly de- 
veloped in those arguments which were discussed under the 
heads of Opposition, Conversion, and Coincident- Junction, 
w^here not only is a premiss not expressed, but it is almost 
unconsciously thought ; so much so, indeed, that it requires 
a searching investigation to become convinced of its exis- 
tence. We need not wonder, therefore, at their being often 
termed immediate inferences. Conditional judgments too, 
are frequently of an enthymematic nature, such as, for in- 
'stance, " If Pegasus be a horse, it must be a quadruped," 
which manifestly proceeds upon the assumption that '' all 
horses are quadrupeds." 

§ 20. Complex Arguments, or Chains of Reasoning, 

It often happens that we arrive at a conclusion through a 
string of correlative syllogisms, and when this is the case we 
have what is termed a chain of reasoning. These arguments 
are, however, generally of an enthymematic form, and are 
divided according as they suppress the conclusion, or one of 
the premises, in each syllogism. 

Those chains of reasoning, where all conclusions but the 
one desired are suppressed, must necessarily consist of pre- 
mises, and this form is known as a sorites. It may be of two 
kinds — first, where the predicate of each premiss is the sub- 
ject of the next succeeding one, and where the conclusion is 
the last predicate affirmed of the first subject ; this is termed 
the ascending, regressive, or Aristotelian sorites: and secondly, 
where the subject of each premiss is the predicate of the next, 
and where the conclusion is the first predicate affirmed of 



SYLLOGISMS. 77 

the last subject ; this is styled the descending, progressive, or 
Goclenian sorites. The formulae of these are : — 

Aristotelian. Goclenian. 

A is B, D is E, 

B is C, C is D, 

C is D, B is C, 

D is E ; A is B : 

.-. AisE. .*. AisE. 

Or, concrete examples may be given, as follows : — 
Aristotelian : — 

Red is a colour, 

A colour is a kind of light. 



All light is a kind of motion ; 
Red is a kind of motion. 



Goclenian : 



AH light is a kind of motion, 

A colour is a kind of light, 

Red is a colour ; 
.'. Red is a kind of motion. 
It will have been observed, that the formula are entirely 
affirmative-; this arises from the rule that we can draw no con- 
clusion from negative premises. We may, however, have the 
last premiss of the series negative, but then the conclusion 
must be negative also, thus : — 

Red is a colour, 

A colour is a kind of light. 

All light is a kind of motion, 

'No motion is material ; 
.*. Red is not material. 
A sorites containing premises of the above description, 
may have its validity directly tested by this modification of 
the dictum : — " Whatever belongs, or does not belong, to a 
given whole, belongs, or does not belong, to each and every 
one of the parts constituting any whole contained in the 
given whole." If, however, the premises are of different forms 
(I, U, &c.), and the reasoning, in consequence, rather com- 
plicated, we may readily ascertain the legitimacy of the 
sorites by a process of dissection ; that is, by resolving it 



78 OF REASONING OR ARGUMENT. 



into its constituent syllogisms. 


The 


formulae for this pur- 


pose are the following : — 








Aristotelian. 






Goclenian. 


A is B, Minor, 






D is E, Major, 


B is C ; Major, 






C is D ; Minor, 


Minor, (.*. A isC), Conclusion. 


■Mp 


jor, 


(.*. C is E), Conclusion. 


Major, C is D ; 


Minor, 


B is C ; 


Conclusion. (.'. A is D), Minor, 


Conclusion. 


(.-. B is E), Major, 


D is E ; Major, 






A is B. Minor, 


.'. A is E. Conclusion. 






.*. A is E. Conclusion. 



From this diagram, it will be seen that each suppressed 
conclusion forms the minor premiss of the succeeding syllog- 
ism in the Aristotelian sorites, and the major in the Goclenian. 
Accordingly, if we detect any false mood among the syllog- 
isms, all its successors will be invalid, as depending upon an 
erroneous premiss. 

A chain of reasoning, wherein one, or more than one 
premiss is suppressed, is termed an epicheirema, and may be 
of three orders ; first, where the major premiss of the main 
syllogism is the conclusion of another syllogism, with but 
one premiss expressed ; secondly, where the minor premiss 
is similarly characterised ; and .lastly, where the conclusion 
forms the sole expressed premiss of a succeeding syllogism, 
a second conclusion thus resulting. The epicheirema may 
also be single, double, or treble, according as it is a combi- 
nation of one, two, or three orders. 

The nature of these arguments will be evident from an 
inspection of the following examples : — 

Single epicheirema of the first order (the major a conclu- 
sion) : — 

All planets are attracted by the sun ; for they revolve 

about him as a centre. 
The earth is a planet ; 
.'. The earth is attracted by the sun. 

Single epicheirema of the second order (the minor a con- 
clusion) : — 

All birds are oviparous, 

The condor is a bird ; for it has wings, feathers, and a 
heart ; 
/• The condor is oviparous. 



SYLLOGISMS. iV 

Single epicheirema of the third order (the conclusion a 
premiss : — 

Matter is imperishable, 
Gold is matter ; 
.'. Gold is imperishable, 

and 
.*. Gold is eternal. 
Treble epicheirema of the conjoint orders : — 
He who is truly wise is just ; for he is virtuous, 
Aristides is truly wise ; for he is led astray by no 
passions ; 
.*. Aristides is just, 

and 
.*. Aristides is happy within himself. 

By symbolising, the last epicheirema may be thus extended 
into complete syllogisms ; the propositions in parentheses being 
those which were suppressed :- — 

^ , . , . ^ ( (All C's are B's) major. 

Conclusion.-A is B | A is C . . . . minor. 

^ , . -i^ . A f (^11 E's are A's) major. 

Conclu8ion.-D is A | D is E . . . . minor. 

.*. D is B minor. 

(All B's are F's) major. 
.*. D is F conclusion. 

The two syllogisms whose conclusions form the premises 
of the main argument, are called prosyllogisms, while the 
syllogism which takes the main conclusion for a premiss is 
termed an episijllogism. 

In the strictest view of the science, pure Logic would take 
no cognisance whatever of incomplete or complex arguments; 
as in them the inference is not necessitated by the mere form 
of the expression. Since, however, all jprac^ica? reasoning is 
of this nature, it would not be advisable to omit its consider- 
ation, as one of our objects is to show the universal extent of 
pure Logic, and also how its laws and principles pervade the 
whole universe of thought. We cannot, therefore, condemn 
the practice of logicians, who almost invariably have dis- 
cussed these reasonings when treating upon the doctrines of 
los^ical elements. 



80 OF REASONING OR ARGUMENT. 

§ 21. Recapitulation, 

We have now concluded our investigation of the principles 
upon which the reasoning process is based, and of its various 
products. I shall, therefore, in accordance with my previous 
practice, briefly recapitulate the principal results at which 
we have arrived. 

Reasoning in general is the eduction of a truth from some 
truths already established, but of whose full import we are 
not aware. It, therefore, cannot be an instrument for the 
extension of science, which would involve the discovery of 
fresh facts, but is of use in the due comprehension and orderly 
arrangement of our knowledge. It also follows that any pro- 
cesss of reasoning (termed a syllogism) is composed of two 
parts — the antecedent, or established truths, and the conclu- 
sion, or truth educed from them. Now the antecedent inva- 
riably consists of tw^o judgments termed premises, but both 
of these are not always articulately enounced. This gives 
rise to a division of arguments into two classes; the one com- 
prising certain syllogisms whose major premiss is always sup- 
pressed ; the other comprising all that remain. The first of 
these classes is divided under three great heads, viz., opposition, 
or the relation subsisting between propositions which differ 
in form, but are identical in matter, such relation being either 
contradictory, contrary, subaltern, or subcontrary ; conversion, 
or the transposition of the subject and predicate in a judg- 
ment, which may be of two kinds, simple and privative ; and 
coincident-junction, or the inseparable union of the attributes 
in a conception. The second class, composed of formal syl- 
logisms, requires as an essential preliminary of its treatment, 
the determination of a fundamental law which may decide 
the validity of all arguments. This law is found to be as 
follows : " Whatever belongs, or does not belong, to the con- 
taining whole, belongs, or does not belong, to each and all of 
the contained parts ; " but, for proximate application, it is 
developed into this canon, *'If tv/o notions agree, either 
wholly or in part, with one and the same third, they agree 
with each otl^er ; but if one of them is agreed, and the other 
disagreed with the same third, they disagree with each other," 



SYLLOGISMS. 81 

which, variously differentiated for particular purposes, enables 
us to test the legitimacy of any syllogism. This canon formed, 
we find that all syllogisms whatever are susceptible of two 
methods of classification ; first, with reference to the position 
of the middle term in the premises, whereby arguments are 
arranged into iowc figures ; and, secondly, with reference to 
the form of the constituent propositions, the symbols repre- 
senting these being grouped in threes, and termed moods. 
This distinction of figure and mood is sufficient as regards the 
form of syllogisms to determine their validity ; but some 
other divisions respecting the import of arguments have a 
claim upon our notice. The doctrines of induction and de- 
duction come first, and apparently depend upon different 
principles, — for induction reasons from the parts to the whole ; 
deduction from the whole to the parts. A close examination, 
however, shows that, as far as ^9i(re Logic is concerned, they 
may be regarded as almost identical. Then follow compre- 
hension (intension) and extension, which respectively interpret 
syllogisms as predicating an attribute of a notion, and a genus 
of a species ; but this distinction also fades into obscurity 
when we reflect upon the irresoluble complexity of our ideas. 
Lastly, we have denomination, which identifies the reasoning 
process as one of naming ; the significance of this interpre- 
tation being merely verbal. Having thus obtained a clear 
notion of the syllogistic theory, by confining our attention to 
arguments composed of categorical propositions, we proceed 
to the consideration of those cases wherein we meet with con- 
ditional judgments ; and, by analysis, we find that they may 
all be referred to these two rules — 1°. '' The antecedent being 
granted, the consequent maybe granted;" and 2°. *^ The 
consequent being denied, the antecedent may be denied.'' 
Next, taking the syllogisms which depend upon disjunctive 
judgments, we find that the principles involved are those of 
a perfect logical division ; while those arguments which fall 
under the name of dilemma may be treated by a combination 
of the rules applicable to each of the two former classes. 
Lastly, we have to examine the popular method of stating 
arguments, and find that they either assume the form of enthy- 
memes, or syllogisms with one proposition suppressed ; or 

e3 



82 OF REASONING OR ARGUMENT. 

else that they are expressed as chains of reasoning, these 
being of two kinds — a sorites, or string of premises with one 
condusion ; and an epicheirema, or syllogism whose premises 
are the conclusions of prosy llogisms, and whose conclusion is 
the premiss of an episyllogism. 

§ 22. Conclusion. 

Here, as stated in the introduction, the province of pure 
Logic terminates ; and if the student has closely followed the 
foregoing analysis of its principles, he will be in a position to 
rightly appreciate its nature and end. Whatever may be the 
ulterior object for which the mind is cultivated, every person 
*• must have thoughts to arrange, knowledge to transplant, 
and facts to record;" and the more effectually these can be 
done, the greater will be the progress. Now, the three great 
instruments for the above-mentioned processes are, first. Logic; 
secondly, languages ; and lastly, the arts of memory.* Thus 
the superiority and precedence of Logic in point of utility is 
apparent : it prepares a sure and solid foundation ; it arranges 
the materials as they arrive in regular courses ; and, finally, 
completes the majestic edifice of a well-ordered mind. Here, 
of course, I allude to the science of Logic ; that is to say, the 
knowledge of the formal laws of thought as applied to the 
treatment of acquired information ; consequently, we must 
not suppose that pure Logic will furnish us with powers of 
observation, or with facts to observe ; its sphere being Hmited 
to the invigoration of those mental abilities with which we 
are respectively endowed, and to the elucidation of those 
truths which have already attracted our attention. It is but 
the few whom Nature has endowed with great intellectual 
power ; and no amount of Logic, or of mental training, will 
supply the original deficiency. A Bacon or an Aristotle is 
born, not made. At the same time, however, the most com- 
manding genius is capable of being raised to a still loftier 

* Compare De Quincey, " Works," vol. xiii. p. 25, who advocates 
these views in a series of Letters, respecting which one can scarce tell 
whether most to admire their purity of style, their elegance of diction, 
their cogency of argument, or their subtle play of humour. 



SYLLOGISMS. 83 

elevation ; as much so as is the weakest mind. We are not, 
therefore, surprised to discover that the names of the most 
sedulous cultivators of Logic are those of the greatest philo- 
sophers that have ever lived. From Socrates, Plato, and 
Aristotle to Bacon ; from Kanada and Gotama to Kant ; 
whether among the academic groves of ancient Athens, the 
busy haunts of British industry, the tropical luxuriance of 
eastern climes, or the ponderous reflections of learned Ger- 
many, there has ever been a bright succession of eminent 
men who have devoted their efforts to the investigation of 
the human mind, its thoughts, their principles, and laws. 
These principles they have employed, not only as regulators 
of the intellect, but also as guides and restraints in their 
search after truth, both moral and physical — such a dispo- 
sition of the science being what is termed applied Logic, 
which will form our next subject of study. 



84: 



CHAPTER V. 



OF FALLACIES. 



§ 1. Applied Logic in General, 

We have now left behind us the sterile, but grand and im- 
pressive realms of theory, and are entered upon the luxuriant 
regions of practice, where there is everything to interest and 
to delight, but whose green and smiKng soil too often hides a 
treacherous morass. Here, then, is the opportunity afforded 
to us of putting our experience to the test, and of deter- 
mining in what way the rules, which we have been acquiring, 
may be of service to us. 

Now, the ultimate end of all thinking, is the attainment of 
truth, and therefore, when we have ascertained what are the 
necessary laws of thought, we should not remain satisfied 
with this speculative knowledge, but should actively employ 
it as a means of advancement towards that higher object for 
which those laws were implanted. This operation it is, 
which forms the province of applied Logic, and which we are 
now about to consider, although the limits of our space must 
necessarily preclude any attempt to do more than take a cur- 
sory — but I trust, instructive — view of so vast a subject. 

I have said that our object now is, to examine into the 
employment of the formal laws of thought as thought, for 
the purpose of attaining truth ; and since we continually 
make use of one fact as a means of arriving at another, it 
follows that the practical application and operation of in- 
ference, must occupy much of our attention. Inference, 
however, may be examined from two points of view, positive 
and nec^ative : for we must either reason correctly or in- 



OF FALLACIES. 85 

correctly : it follows, therefore, that the spheres of investigation 
which present themselves are — first, the essential conditions of, 
and inducements to, a legitimate inference ; and secondly, the 
causes and nature of an illegitimate inference. The question 
now comes, w^hich of these subjects shall we first examine ? 
and the ratio decidendi must be the end which we propose to 
ourselves: this is the acquirement of truth, and can only be 
attained by a proper understanding of what constitutes cor- 
rect inference. But, in order to properly understand what a 
thing is, we should first ascertain what it is not ; for, as Bacon 
says, ** Inductio quae ad inventionem et demonstrationem 
Scientiarum et Artium erit xitilis, Naturam separare debet, per 
rejectiones et exctusiones dehitas ; ac deinde post negafivas tot 
quot sufficiunt, super affirmativas concludere." Accordingly, 
our immediate duty must be to investigate the conditions 
and concomitants of incorrect inference, or ^' bad reasoning," 
as it is generally termed. 

Every argument consists in drawing a conclusion from 
certain evidence which has been adduced, and if this evidence 
be such as to warrant the conclusion, we are said to reason 
legitimately ; if not, the reverse. Now, as no man ever 
assents to a judgment unless he deems its evidence conclusive, 
a case of false reasoning can only occur where the evidence, 
though seemingly just and sufficient, is, in reality, fallacious 
and deceptive ; such an argument is called sl fallacy. 

§ 2. Classification of Fallacies. 

The true w^ay of comprehending any subject is — as we 
discovered when treating upon pure Logic — to arrange it in 
a system constructed upon the principles of logical division 
and classification. It, therefore, behoves us, if we would 
make a practical use of the science, to at once arrange the 
various fallacies under their respective heads, before proceed- 
ing to discuss them in detail. 

Every syllogism consists of two parts, form and matter : 
this enables us to divide ail fallacies into two great classes, viz., 
those whose inference is erroneous, through being informally 



86 OF FALLACIES. 

expressed ; and those where the premises legitimately imply 
the conclusion, if the form of the syllogism be alone regarded, 
but where an examination of the matter will show the reason- 
ing to be invalid. 

Formal fallacies are those which violate the syllogistic 
canons, and may be subdivided into as many co-ordinate 
species as there are proximate rules. It will only be neces- 
sary, however, for our purposes, to regard the faults of un- 
distributed middle and illicit process. 

Material fallacies may be erroneous, either as regards 
their terms, their premises, or their conclusion, and are con- 
sequently subdivided into these three subaltern genera, viz., 
quateimio terminorum, or syllogisms with four terms ; syllo- 
gisms with a premiss unduly assumed ^ and ignoratio elenchi, 
or syllogisms which do not prove the required conclusion. 

The species of these subaltern genera, may be arranged 
in accordance with the following considerations : — 

1^. Quaternio terminorum. This fallacy may arise from 
the ambiguity of the middle term, so that in the major pre- 
miss one sense of the word is used, in the minor, another. 
Or, for any one of the terms, two words may be employed 
which are supposed to imply the same meaning, but do not. 
Or, again, a term may consist of several notions, these being 
taken together in one judgment, and separately in the other. 
Or, lastly, a term may be used absolutely in one judgment, 
and relatively in the other. 

2°. A premiss unduly assumed. The causes of this may 
be, — considering certain truths as self-evident w^hich are not 
so ; forming a judgment from some pre-conceived opinion, 
false analogy, or false generalisation ; over-estimating the 
weight of probabilities ; reasoning in a circle ; or, taking 
for a premiss some proposition which is the same as, or im- 
plies, the conclusion. 

3°. Ignoratio elenchi. This occurs whenever appeals are 
made to the passions, prejudices &c., of men ; when a part is 
proved instead of the whole ; &c., &c. 

The foregoing division may be exhibited in a *' scheme," 
as follows : — 



OF FALLACIES. 



87 



Fallacies 
are 



Formal 



f Undistributed middle. 
(_ Illicit process. 



> Material 



f Ambiguous middle. 

J Fallacia figures dictionis. 

I Fallacia sensus compositi 
ei divi i. 

I Fallacia a dido secun- 
dum^ &c. 

A priori fallacies. 

Fallacies from pre-coz- 
ceived opinions. 

From false analogies. 

From false generalisa- 
tions. 

False estimation of pro- 
babilities. 

Reasoning in a circle. 

Petitio principii (" beg- 
ging the question.") 



(Argumenta ad hominerriy 
Ignoratio ) d:c. 
elenchi j Part for whole. 
( <fec. &c. 



/ Quaternio 
terminorum 



Premiss 
unduly 
assumed 



Before we commence the discussion of each of the above 
fallacies in its order, it may be well to remark that the above 
division could only be logically perfect, provided we were 
allowed to make arbitrary distinctions between individual 
examples of false reasoning ; for there are some fallacies 
which belong to one species equally as much as they do to 
another. This, in many cases, arises from the enthymematic 
mode of expression which obtains so universally : were a man, 
for example, in maintaining the efficacy of imprisonments for 
life, to argue that ^' capital punishment is improper," because 
*' it does not tend to make the criminal a better member of 
society, " we must either suppose him to hold that '* a?/ proper 
punishments are for the purpose of reformation, as regards 
the criminal's social behaviour," or that some are. In the 
former case, the complete syllogism would run thus : — 

All proper punishments are intended for the criminal's 

social reformation, 
Capital punishment is not so intended ; 

.*. Capital punishment is improper. 

Here the formal reasoning is perfectly vaHd, but when 
the matter is examined, we see that the major premiss is un- 
duly assumed ; for, obviously, imprisonment for Ii/e is not 
intended to make the criminal a better member of society, as 
it starts with the condition that he shall never mix with his 
fellow-creatures a£?ain. 



88 OF FALLACIES. 

If WG adopt the latter of the suppositions stated above, the 
argument will be as follows : — 

Some proper punishments are intended for the criminal's 

social reformation, 
Capital punishment is not so intended ; 

/. Capital punishment is improper ; — 
where there is an illicit process of the major term, and, con- 
sequently, a formal fallacy. 

In cases similar to the foregoing, it must always remain 
doubtful as to which class they belong ; and, therefore, the 
division adopted must be considered as only approximatively 
correct. This state of things, however, obtains in every 
science, and arises from the necessary imperfection of our 
knowledge : in chemistry, for instance, it is a moot point as 
to whether arsenic should be included amongst the metallic 
or non-metallic elements ; while, in biology, it is almost im- 
possible to draw the line between animal and vegetable life. 
At the same time, most classifications are correct enough 
for all practical purposes, if not in strict accordance with the 
rigorous requirements of theoretical truth. Thus much pre- 
mised, we shall now enter upon a detailed account of the 
various species of fallacies. 

§ 3. Formal Fallacies, 

These, as already stated, consist of such syllogisms as 
violate the canons which have been laid down for the purpose 
of determining the validity of an argument from its form. 
The principal species are Undistributed middle, and Illicit 
process. Examples may be thus given : — 
Cndifetributed middle: — 

Negroes are men, 
Hindoos are men ; 
.-. Hindoos are negroes. 
Illicit process : — 

All planets revolve round the sun, 
All planets are stars ; 
.*. All stars revolve round the sun. 
The subject of form has been so fully discussed in the pre- 
ceding chapter, that it will not be necessary to add anything 



OF FALLACIES. 89 

further upon this point. The following observations, how- 
ever, taken from Archbishop Whately*s "Elements," are of 
great importance. 

" To the present class [formal fallacies] we may the most 
conveniently refer those fallacies, so common in practice, of 
supposing the conclusion false because the premiss is false, or 
because the argument is unsound ; and of inferring the truth 
of the premiss from that of the conclusion, e.g., if any 
one argues for the existence of a God, from its being uni- 
versally believed, a man might, perhaps, be able to refute the 
argument by producing an instance of some nation destitute 
of such belief; the argument ought then to go for nothing : 
but many would go further, and think that this refutation 
had disproved the existence of a God ; in which they would 
be guilty of an ilHcit process of the major term : viz., * What- 
ever is universally believed must be true ; the existence of a 
God is not universally believed ; therefore, it is not true.' 
Others again, from being convinced of the truth of the con- 
clusion, would infer that of the premises, which would 
amount to the fallacy of an undistributed middle : viz., 
* What is universally believed is true ; the existence of a God 
is true ; therefore, it is universally believed.' Or, these 
fallacies might be stated in the hypothetical form ; since the 
one evidently proceeds from the denial of the antecedent, to 
the denial of the consequent ; and the other, from the estab- 
lishing of the consequent, to the inferring of the antecedent ; 
which two fallacies will usually be found to correspond re- 
spectively with those of Illicit process of the major, and 
Undistributed Middle. 

** Fallacies of this class are very much kept out of sight, 
being seldom perceived even by those who employ them ; but 
of their practical importance there can be no doubt, since it 
is notorious that a weak argument is always, in practice, 
detrimental; and that there is no absurdity so gross which 
men will not readily admit, if it appears to lead to a con- 
clusion of which they are already convinced. Even a candid 
and sensible writer is not unlikely to be, by this means, mis- 
led, when he is seeking for arguments to support a conclusion 
which he has long been fully convinced of himself; ^.e., he 



90 OF FALLACIES, 

will often use such arguments as would never have convinced 
himself, and are not likely to convince others, but rather (by 
the operation of the converse Fallacy) to confirm, in their dis- 
sent, those who before disagreed with him." 

§ 4, Material Fallacies : Quaternio Terminoritm, .. 

1°. Ambiguous middle. This occurs whenever one sense 
of the middle term is employed in the major premiss, and 
another in the minor, thus — 

Whoever is nervous is timid, 
Hercules was nervous ; 
/. Hercules was timid. 

The word nervous is here used in two senses, viz., " timid " 
and ^* strong," and, consequently, the syllogism contains four 
terms, which, of course, renders it invalid. I have given an 
example in which the error may be easily perceived, but it 
must not be supposed from this, that all cases of ambiguous 
middle are of such a simple character. Indeed, there are 
many words of common use, which continually give rise to 
mistaken ideas in consequence of their ambiguity. Thus, the 
impression is very general, that the " men of old " were 
superior in wisdom and experience to those of modern times ; 
this notion arising from the natural reverence which we feel 
for the opinions of '' old men,'' in consequence of their longer 
life having enabled them to form a better judgment of the 
world's course than younger men can do. Of course, when 
the syllogism is fully expressed — " Old men are worthy of 
reverence; these men are men of old; therefore, these men are 
worthy of reverence" — we see at once that the word old is 
used at one time in the sense of aged, and at another^ as 
signifying removed from us hi/ length of time ; and that, 
accordingly, the reasoning is inconsequent ; but then we 
must remember that arguments, in practice, are elliptical, 
the premises being oftener hinted at, than articulately stated. 
A skilful sophist, therefore, will avoid anything like a defini- 
tion of the terms he employs, or a full expression of his in- 
ference ; trusting to the various associations, traditions, and 
prejudices of his hearers to supply such ideas as may be best 



OF FALLACIES. 91 

calculated to lead them to the desired conclusion. And in 
like manner, it follows that the most effectual remedy against 
fallacies of this description, is to insist upon a precise expla- 
nation of the sense in which each term is nsed. That this 
caution is not unnecessary, will easily be seen if we reflect 
upon the great number of words which are susceptible of 
duplicate, triplicate, &c., interpretations ; e.g., law may mean 
either a command for persons to obey, or a general expression 
for a group of physical facts ; same implies identicality, and 
also great similarity ; may and can, sometimes signify liberty, 
and sometimes possibility, &c., &c. 

2°. Fallacia figures dictionis. It frequently happens that 
pavonijmous words, i.e., those which have a grammatical 
relation to each other in consequence of their springing 
from the same root, differ considerably in meaning, but yet 
in the haste of an argument are assumed to be of similar 
import. This produces what the old logicians have termed 
the fallacia figurce dictionis, and is dangerous on account 
of the many variations which may be, and commonly are, 
given to a term in the course of a chain of reasoning, with- 
out infringing the validity of the conclusion. Thus, it 
would be perfectly allowable to say, ^' Wherever a lighted 
candle maintains great luminosity, the atmosphere is respir- 
able ; in this well a lighted candle continues to be very lumi- 
nous ; therefore, here the atmosphere is respirable ;" for the 
expressions ^^ to maintain luminosity " and '' to continue lumi- 
nous " are justly treated as equipollent : but were we to say, 
" No designing persons are honest ; all sculptors design ; 
therefore no sculptor is honest," we should in reality employ 
four terms ; " designing " meaning scheming ox plotting, while 
*' to design " implies the conception of some idea to he executed 
hij an artist. 

The proper method of combating this fallacy consists in an 
explanation of the different senses attaching to the parony- 
mous words. 

3°. Fcdlacia sensus compositi et divisi. This, which is also 
termed the fallacy of composition and division, is produced 
whenever a term is used in one judgment collective! i/, and 
in the other distrihutiveli/, A simple example is as follows : — 



92 OF FALLACIES. 

** Five and two are odd and even ; seven is five and two ; 
therefore, seven is odd and even." Here "five and two" 
means in the major premiss, those numbers alluded to 
distinctly and respectively ; in the minor, the same taken 
together ; accordingly, there is a case of quaternio termi- 
normn. 

Perhaps the most frequent method of employing fallacies of 
this description, is when a truth which has been separately 
established concerning many individual notions is sought to 
be inferred of them ail collectively. Thus it is occasionally 
argued, that because the ordinary alterations of temperature 
produce comparatively little effect upon the physical configura- 
tion of the earth's surface, and because the same thing may 
be asserted of each of the natural disintegrating and abrading 
powers, such as tides, rivers, rain, glaciers, &c., therefore the 
combined operation of all together would not do more, and, 
consequently, that we must assume some grand cataclysm as 
the cause of such great changes as may be apparent. 

In all cases of probabiHty there is often a tendency to fall 
into the error now under consideration, and this tendency is 
in opposite directions. Suppose we are told that it is an even 
chance whether the disease upon reaching a certain stage will 
kill the sufferer or not ; and, also, that it is an even chance 
whether the disease will reach that stage ; we are apt to con- 
clude that an even chance results of the person dying or not 
dying ; whereas the chances are three to one against his 
dying. This is rendered evident as follows : the chance of^ 
the disease reaching a certain point is one-half of all the pos- 
sible changes which may supervene ; but the chance of dying 
is only one-half of these, i.e., one-quarter of the possible cases ; 
therefore the chance of not dying is three-quarters, or in the 
ratio of three to one. Here the probability was over-esti- 
mated, but in many instances the reverse is the case : thus, 
if we were to argue, that because it is improbable that the 
whole of Newton's discoveries were the results of fortunate 
coincidences, it is, therefore, improbable that any one of them 
was so, we should commit this error. 

Archbishop Whately under this head describes what he 
terms the thaumatrojpe fallacy; this consists in presenting 



OF FALLACIES. C'3 

several incompatible notions to the mind in quick succession, 
so as to induce the belief that they might exist together. 
After the Crimean war, for example, a statement was pub- 
lished showing the several objects which the money spent 
might have separately accomplished. Now, in all probability, 
many persons on reading the long list, and finding that this, 
that, and the other thing might have been done, left off with 
the idea that all of these objects together were capable of 
realisation. 

4^. Fallacia a dicto secundum, dhc. These fallacies arise 
when we conclude absolutely of a notion what is true of it 
only under certain circumstances ; and when we conclude 
relatively what is only true when absolute ; the latter is 
sometimes termed fallacia accidentis. 

Persons occasionally fall into this error when arguing 
against capital punishment, forming their syllogism thus : — 
To return evil for evil is wrong. 
Capital punishment is returning evil for evil ; 
.*. Capital punishment is wrong. 
Here the major premiss is only true under certain qualifica- 
tions ; that is to say, a revengeful animus is supposed in com- 
bination with returning evil for evil ; whereas in the minor, 
the action is considered in the abstract, and without any such 
attendant circumstance. 

Again, uneducated people are greatly astonished upon 
being told that the earth is nearer to the sun in winter than 
in summer, for their thoughts immediately run in this fashion; 
*' the nearer we are to a hot body the warmer we must be, 
and therefore the earth ought to become warmer instead of 
colder on approaching the sun.'* The mistake, of course, 
lies in their ignorance of the fact that we only get warmer 
upon approaching a hot body ^provided that the rays' of heat 
continue to strike us at the same, or at a more favourable 
angle. 

Fallacies of this nature are very difficult to detect, in con- 
sequence of the readiness which exists to lose sight of the 
limitations which alone render a general law capable of being 
applied to some particular case. The best method of treatment 
is to require a rigid proof of both premises, which will always 



94 OF FALLACIES. 

exhibit whether the inference is legitimated by the circum- 
stances of the case. 

The false reasonings which have been described above 
are the principal fallacies belonging to the genus of quaternio 
terminorum ; but there are many various ways of sophistica- 
tion by means of ambiguity in expression, which, though 
not syllogistic, are often employed. Such is the practice of 
asking a question that may be susceptible of various interpre- 
tations according to the answer given ; e.g., an opponent of 
free-will might ask, " Am I free to do as I please ?" and, 
being answered in the affirmative, would reply, ^' Then I am 
at liberty to kill you and half-a-dozen more if I so please." 
If answered in the negative, he would at once say, ** Then I 
am controlled by necessity, and am not a free-agent." In 
this instance the ambiguous word is " free," which in one 
case is held to mean '* free as regards nature ;" in the other, 
" free as regards the laws of society." The student will have 
no difficulty in forming the corresponding syllogisms. 

Perhaps, however, the most celebrated fallacy depending 
upon the ambiguity of a word, is the sophistical puzzle of 
Achilles and the tortoise. Its enunciation and solution are 
given by Mr. Mill as follows : — 

'* The argument is, let Achilles run ten times as fast as the 
tortoise, yet if the tortoise has the start, Achilles will never 
overtake him. For suppose them to be at first separated by 
an interval of a thousand feet : when Achilles has run these 
thousand feet, the tortoise will have got on a hundred ; when 
Achilles has run those hundred, the tortoise will have run 
ten ; therefore, Achilles may run for ever without overtaking 
the tortoise. 

'* Now, the * for ever' in the conclusion, means, for any 
length of time that can be supposed; but in the premises 'ever' 
does not mean any length of time : it means any number of 
subdivisions of time. It means that we may divide a thou- 
sand feet by ten, and that quotient again by ten, and so on as 
often as we please ; that there never needs be an end to the 
subdivisions of the distance, nor, consequently, to those of 
the time in which it is performed. But an unlimited number 
of subdivisions may be made of that which is itself limited. 



OF FALLACIES. 95 

The argument proves no other infinity of duration than may 
be embraced within five minutes. As long as the five 
minutes are not expired, what remains of them may be divided 
by ten, and again by ten, as often as we like, which is per- 
fectly compatible with their being only five minutes alto- 
gether. It proves, in short, that to pass through this finite 
space requires a time which is infinitely divisible, but not 
an infinite time." 

Another example of the same fallacy may be thus given : 
If at present we look forward into eternity we see that the 
duration yet to come is infinite ; but the same state of things 
will obtain a hundred years hence, and as two infinite dura- 
tions must be equal to each other, the futurity then, and the 
futurity now cannot differ ; therefore the hundred years con- 
stitute no lapse of time whatever, as otherwise there would 
be a difference of so much between the periods in question. 
Thrown into a syllogistic form the argument would stand 
as follows : — 

Two infinite durations are equal to each other, 
The present futurity, and the present futurity less a 
hundred years, are two infinite durations ; 

.*. The present futurity is equal to the same, less a hundred 
years. 

Here the major premiss involves a contradiction in terms, 
for it implies that two mcommensurahle things (i.e., two dif- 
ferent infinities) are commensurahle ; it is, therefore, inadmis- 
sible. Or the solution might pass were w^e to say that the 
middle term is ambiguous, meaning in the major premiss, "two 
infinite durations starting from the same point,'' and in the 
minor, "two infinite durations starting from different points!' 

§ 5. Material Fallacies : Pre^niss unduly assumed. 

1^. A priori fallacies. We have now to consider those 
errors which arise from the assumption of a premiss, either 
without any proof at all, or without such proof as would be 
considered sufficient by both parties, if they were equally 
apprised of the questions at issue. And first, of those cases 
whjRre there is no proof whatever of the assumed premiss. 



lb OF FALLACIES. 

As an essential preliminary, it must be remarked that there 
are some truths which we do not attain by any reasoning 
process,* and which, therefore, are not susceptible of proof. 
Thus, when a piece of brass engages my attention, I am con- 
scious of some change which takes place in my mind, and 
this change I call the sensation of yellow, applying the name 
yellow to those attributes of the brass which produced the 
sensation ; therefore, when I say, ** This brass is yellow,'* I 
cannot abstractedly prove the statement, as I am merely 
asserting a subjective fact, of whose existence I alone can 
judge, and which is only granted by my opponent in con- 
sequence of his being affected by similar sensations. Accord- 
ingly, such truths are termed self-evident, and must form the 
foundation of all reasoning. 

This consideration is the clue which guides us to the source 
of the particular class of sophisms at present under investiga- 
tion. Men, finding that certain of their sensations corre- 
spond with outward facts, go further, and imagine that 
whenever any subjective state of consciousness is ascertained, 
there must always exist a correlative condition of the objects 
about which thought is concerned. Thus, Philolaus and 
the Pythagoreans, imagining that the nature of fire was 
more incomprehensible than that of earth, and feeling that 
whatever they could least comprehend impressed their minds 
with the greatest sensations of awe, concluded that fire 
in itself was more capable of majesty than earth, and in the 
disposition of the universe would occupy the most worthy 
place. Accordingly, they conceived that there existed in 
the centre of the universe a mass of fire termed the " Altar 
of Nature," and that, at distances varying with the dif- 
ferent degrees of fiery composition, were ranged the heaven 
containing the fixed stars, the planets, and all other cosmical 
bodies. 

Perhaps the most prevalent class of a priori fallacies is that 
which results from an inspection of the imaginative powers, 
it being assumed that objective existence is dependent upon 

* A practical view. Compare with this the section upon Obser- 
vation. 



OF FALLACIES. 97 

the possibility or impossibility of its being conceived by us. 
Dr. Clarke, for instance, in a correspondence with Bishop 
Butler, makes use of the following expression, " The suppos- 
ing anything possibly to exist alone, so as not necessarily to 
include the pre-supposal of some other thing, proves demon- 
strably that that other thing is not necessarily existing ; 
because whatever has necessity of existence cannot possibly, 
in any conception whatsoever, be supposed aw^ay." Here the 
statement is implied that because we cannot conceive it, there- 
fore, no necessary existence can be apart from or indepen- 
dent of any other existence ; this, of course, being an arbi- 
trary assumption that the laws of our minds regulate the 
facts of nature. 

Again, one of the most celebrated modern systems of phi- 
losophy was based upon this error; viz., that of Descartes, 
concerning whom Mr. Mill speaks thus : — '' His favourite 
device for arriving at truth, even in regard to outward things, 
was by looking into his own mind for it. ' Credidi me,' says 
his celebrated maxim, ' pro regula generali sumere posse 
omne id quod valde dilucide et distincte concipiebam, verum 
esse :* whatever can be very clearly conceived must certainly 
exist ; that is, as he afterwards explains it, if the idea includes 
existenae. And on this ground he infers that geometrical 
figures really exist, because they can be distinctly conceived. 
Whenever existence is * involved in an idea,' a thing con- 
formable to the idea must really exist — which is as much as 
to say, whatever the idea contains must have its equivalent in 
the thing ; and what we are not able to leave out of the idea 
cannot be absent from the reality. This assumption pervades 
the philosophy not only of Descartes, but of all the thinkers 
who received their impulse mainly from him, in particular 
the two most remarkable among them, Spinosa and Leibnitz, 
from whom the modern German metaphysical philosophy is 
essentially an emanation."* 

Locke, too, founds his proof of the existence of a God upon 
the considerations, that as (se]f-evidently) nothing cannot 
produce any real being, something must have existed from all 

* *' Logic," book V. chap. iii. § 3. 

F 



98 OF FALLACIES. 

eternity ; and that this something must be a cogitative being, 
because it is as impossible to conceive that every bare incogi- 
tative matter should produce a thinking intelligent being, 
as that nothing should of itself produce matter. This reason- 
ing hinges upon the supposition that '' what is inconceivable 
is impossible,'* a proposition which is continually being dis- 
proved as knowledge advances, and our means of investigation 
become greater. In fact, that great truth which is ever 
present with us — the action of mind upon matter — should of 
itself suffice to overthrow all reliance upon any necessary con- 
nection between subjective and objective existences. 

An ordinary case of the operation of the above fallacy is to 
be found in the reception accorded to any account of won- 
derful events. Take, for example, the case of mesmerism, or 
spirit-rapping. One person cannot conceive the possibility 
of the facts being produced by ordinary means, and, therefore, 
assumes that they must be the results of supernatural agency ; 
w^hile another, not being able to imagine that immortal beings 
would, or that mortals could, give rise to such events, con- 
cludes that these cannot have occurred. In each extreme 
an erroneous inference takes place, founded upon a premiss 
unduly assumed. 

Another duplicate group of errors is based upon the sup- 
positions that nothing can be true unless some reason can be 
assigned for it, and that everything must be true if there 
exist no reason against its being so. To the former may be 
referred the usual objection of '^ cuihonoV which assumes 
that an objective fact does not exist if its practical uses arc 
not immediately observable. To the latter belong most of 
the a priori demonstrations of physical truths, one of the best 
known being Duchayla's proof of the composition of forces, 
w^hich rests upon the axiomatic statement that " the resultant 
of two forces meeting at a point, must bisect the angle 
betw^een them." This is said to be self-evident, '^ because toe 
can assign no reason why the resultant should incline to one 
force rather than to the other." Here, as all a priori reason^ 
ing is necessarily anterior to experimental knowledge, we 
cannot be certain but that something may exist in the natural 
action of two forces upon each other, which shall invariably 



OF FALLACIES. 93 

incline their resultant to the right or to the left; nor can 
any reason be assigned for the resultant bisecting the angle, 
rather than inchning to one of the forces. The first step, 
therefore, of the proof being unfounded, the remaining por- 
tions are untenable ; and, indeed, it would appear generally 
true, that the only valid reasoning with reference to physical 
facts is such as may be deduced from experiment, i.e., such 
as is a posteriori. 

A very ancient example of the fallacy which we have just 
considered is to be found in the astronomical doctrines of 
Anaximander, who flourished at the commencement of the 
sixth century, b.c. He held that the earth was suspended 
immovably in space, because^ "being equidistant from the 
containing heaven in every direction, there was no reason 
why it should move in one direction rather than in another." 

There remains but one more species of a priori fallacies to 
which I shall allude, viz., those arguments which rest upon 
the suppositions that an effect has but one cause, and that 
causes must resemble their effects. Thus, Plato,* in one of 
his dialogues, makes Socrates give an account of an investi- 
gation into the causes of things, which results in the conclu- 
sion that every phenomenon has its own single and separate 
cause — a substance being red, because a certain abstract 
'^ redness " dwells in it ; large, because an abstract " magni- 
tude " is present; small, on account of 'littleness;" and so 
on. This opinion pervaded all philosophy until the days of 
Bacon, who, by his advocacy of experiment, led the way 
towards the admission that the same effects may be produced 
by different causes. At the same time, however, it is to be 
remarked that even Bacon himself was not altogether free 
from these errors, inasmuch as in his celebrated inquiry con- 
cerning the " form," or nature of heat, he assumes that the 
sensation of heat is always caused by the same set of condi- 
tions or attributes, whereas we now know that intense cold 
(and other causes) will produce a similar effect as far as our 
feehngs are concerned. He also imagines that there must be 



* Sir G. C. Lewis's '* Astronomy of the Ancients," chap. ii. § 5, 
t "Ph£edo," § 103. 

F 2 



100 OF FALLACIES. 

a resemhiance between causes and effects, for we find him 
speaking as follows :* — ^' Heat is a motion of expansion, not 
uniformly of the whole body together, but in the smaller parts 
of it ; and at the same time checked, repelled, and beaten 
back, so that the body acquires a motion alternative, per- 
petually quivering, striving and struggling, and irritated hy 
reipercibssion, whence springs the furi/ of fire and heat." 
Hence it is that, although very near the mark, he has yet 
failed to obtam a clear and comprehensive notion of heat, for 
he says,f " Again, it [that heat is a motion of constituent 
atoms, not of constituted bodies] is shown in this, that when 
the air is expanded in a calender glass, without impediment 
or repulsion, that is to say, uniformably or equably, there is 
no perceptible heat. Also, when wind escapes from confine- 
ment, although it burst forth with the greatest violence, there 
is no very great heat perceptible, because the motion is of 
the whole, without a motion alternating in the particles." 
Here, from the assumption that the sensation of heat must 
always be produced by heat, he concludes the absence of the 
latter in cases where we know it is really present. The rea- 
son, then, of Bacon's failure would appear to be that he con- 
fined himself to the investigation of the nature of that set of 
conditions which are capable of producing the sensation of 
heat ; whereas he should have endeavoured to ascertain the 
number of different effects which might be produced by the 
action of heat : " the power of artificially producing an effect," 
as Mr. Mill says,J *'' implying a previous knowledge of, at least, 
one of its causes. If we discover the causes of effects, it is 
generally by having previously discovered the effects of causes." 

I have considered these a priori fallacies at some length, 
in consequence of their universal influence, and small liability 
of detection. The remedy is to deny the self-evidence of the 
assumed principle, and require a proof. 

2°. Fallacies from pre-conceived opinions. It often hap- 
pens that men are content to accept, as estabhshed truths, 
assertions whose only foundations are derived from their 

* " Nov. Org.," book ii. Aph. 20. Spedding's Trans. f Ibid, 

f " Logic," book V. chap. iii. § 7. Compare with preceding remarks. 



OF FALLACIES. 101 

consonance with some pre -conceived opinion, or from a hasty 
inspection of the facts involved. x\nd in cases where an 
intentional piece of sophistry is employed, the most suc- 
cessful plan is to mention the premiss as something wonderful 
and surprising ; the effect of which is that our attention is 
no longer directed to the question of the proposition's truth 
or falsity, but rather to the best method of accounting for the 
fact.^ Thus, the Eoyal Society were, for a long time, puzzled 
by King Charles II.'s inquiry, as to the reason why a dead 
tish will not add to the weight of a vessel of water, although 
a lice fish will ; and it was not until after many vain attempts 
to discover a solution of this marvel, that the philosophers 
remembered that there might be a doubt as to whether it 
existed at all. 

Most cases of superstitions may be referred to this head ; 
that is to say, most instances of superstitious belief producing 
any. effect upon the mind. How many reputed supernatural 
appearances would have been investigated, and their real 
nature detected, if the prevalent belief that such events were 
of frequent occurrence, had not precluded the necessary ex- 
amination ! And even to the present day, there are persons 
to be found in provincial districts, who will attribute any 
sudden misfortune to the operation of witchcraft, simply be- 
cause they have always understood that this power was the 
usual cause of similar events ; never deeming it necessary to 
ascertain the truth of the tradition. 

Indeed, there would seem to exist some faculty in the 
mind which renders us disposed to accept whatever is handed 
down in the shape of tradition, the more especially if it be 
of prodigious and marvellous import. Possibly the fact is, 
that the majority liave a great disinclination to exert their 
mental powers more than is absolutely required for the proxi- 
mate objects of their pursuits ; and, consequently, they regard 
with disfavour any attempt to disabuse them of erroneous 
opinions, as such a course would necessarily involve the 
exertion of accustoming themselves to new methods of belief. 

"d^. Fallacies from fcdse analogies. Analogy is, properly 

* Compare Whately's " Logic,"' book iii. § 14. 



102 OF FALLACIES. 

speaking, a '^ resemblance of relations :" and when '^ we argue 
from analogy," we assert that two objects which resemble 
each other in one point, will also resemble each other in 
another point, w^hich depends in both cases, by a similar 
relation upon the first. Thus, we conclude that ammonium 
is a metal, because it resembles other metals in its forma- 
tion of an amalgam with mercury ; that is to say, the rela- 
tion between the constituents of each amalgam, being pre- 
cisely similar, we infer that they are severally composed of 
mercury, in combination with a metal.* But were we to infer 
that sulphur is a metal, because heat vaporises it as well as all 
metallic substances, we should be employing a false analogy, 
because the relation of vaporisation does not necessarily 
determine the presence of a metal in conjunction with heat. 

Accordingly, a fallacy of false analogy may be considered 
to exist wherever from a resemblance in one point is inferred 
a resemblance in another, without, at the same time, its being 
shown that there exists a similarity of relations between the 
two points. 

Professor De Morgan notices the following prominent in- 
stances of this fallacy* : — *' All the makers of systems, who 
arrange the universe, square the circle, and so forth, not only 
comfort themselves by thinking of the neglect which Coper- 
nicus, and other real discoverers, met with for a time, but 
sometimes succeed in making followers. These last forget 
that for every true improvement, which has been for some 
time unregarded, a thousand absurdities have met that fate 
permanently. It is not wise to toss up for a chance of being 
in advance of the age, by taking up at hazard, one of the 
things which the age passes over. As little will it do to 
despise the usual track for attaining an object, because 
(as always happens) there are some who are gifted with 
energies to make a road for themselves. Dr. Johnson tells a 
story of a lady who seriously meditated leaving out the classics 
in her son's education, because she had heard Shakspeare 
knew little of them. Telford is a standing proof (it is sup- 
posed by some) that special training is not essential for an 
engineer." 

* " Formal Logic," p. 276. 



OF FALLACIES. 103 

In Plato's '^ Dialogue upon the Immortality of the Soul," 
Simmias objects that, according to Socrates' account, the 
soul is a harmony of the body, and that therefore, it will be 
destroyed when the body is, in the same manner as the har- 
mony of a lyre ceases when the lyre is broken. But Socrates 
shows the fallacy of this argument, by pointing out that the 
same relation does not obtain between the soul and body, as 
between the lyre and its harmony ; for, as had been pre- 
viously granted, the soul exists before the body, and is, there- 
fore, independent of it, w^hile the harmony of any particular 
lyre cannot exist until the instrument is constructed, and 
accordingly perishes when it is destroyed. 

The records of ancient astronomy abound with examples 
of fallacious analogies. The Pythagoreans, for instance, are 
reported by Aristotle, to have conceived that ten was the 
only perfect number, and, therefore, the number of bodies 
revolving round the central fire must also be ten. But nine 
only were visible to them ; viz., the sun, the moon, the earth, 
the five planets, and the sphere of fixed stars ; accordingly, 
they imagined another, which they termed the antichthon, 
and declared to be invisible from the earth, as it was upon 
the opposite side to the inhabited portion. In like manner, 
the distances of the several orbits were assumed to increase 
constantly, in the ratio of three to one, a calculation which 
made the sun's distance from the centre 729 : this number 
being both a square and a cube, the sun also was said to be a 
square and a cube. " Finding that the distances of the 
planets bore, or seemed to bear to one another, a proportion 
not varying much from that of the divisions of the mono- 
chord, they inferred from it the existence of an inaudible 
music, that of the spheres : as if the music of a harp had 
depended solely on the numerical proportions, and not on the 
material, nor even on the existence of any material — any 
strings at all. It has been similarly imagined that certain 
combinations of numbers, which were found to prevail in 
some natural phenomena, must run through the whole of 
nature : as that there must be four elements, because there 
are four possible combinations of hot and cold, wet and dry ; 
that there must be seven planets, because there were seven 



104 OF FALLACIES. 

metals, and even because there were seven days of the week. 
Kepler, liimself, thought there could be only six planets, 
because there were only five regular solids."* Nor must it 
be imagined that these fantasies are confined to the olden 
times, for I, myself, have heard a clergyman seriously main- 
tain, from the pulpit, that the number seven must be sacred 
in its nature, because it is composed of three and four ; the 
former representing the Holy Trinity ; the latter, man and 
nature, all of whose attributes and members are regulated by 
twos and fours. 

** Another example is the not uncommon dictum, that 
bodies politic have youth, maturity, old age, and death, like 
bodies natural — that after a certain duration of prosperity 
they tend spontaneously to decay. This also, is a false an- 
alogy, because the decay of the vital powers in an animated 
body, can be distinctly traced to the natural progress of those 
very changes of structure, which, in their earlier stages, con- 
stitute its growth to maturity; while in the body politic, the 
progress of those changes cannot, generally speaking, have 
any effect but the still further continuance of growth : it is 
the stoppage of that progress, and the commencement of re- 
trogression, that alone would constitute decay. Bodies politic 
die, but it is of disease, or violent death : they have no old 
age."t 

Fallacies of false analogy may be shown to be erroneous, 
by proving that there is no causative connection between 
the resemblance observed and the resemblance inferred ; or, 
in other words, that it does not necessarily follow that they 
must always co -exist. 

4°. Fallacies from false generalisations. Numerous causes 
exist, which lead us to infer universal propositions where 
only particular ones are warranted by the facts of the case. 
Memory itself is an active agent in promoting this error ; as, 
for instance, in the case of predictions being verified, marvel- 
lous coincidences, and the like, we only remember those 
occurrences where the prediction was fulfilled, or where some 
result followed the coincidence, and entirely forget those of 

* Mill's " Logic," book v. chap. v. § 6. 

f Mill's '^ Logic," book v. chap. v. \ 6. ^ 



OF FALLACIES. 105 

the contrary nature. We then enumerate the remembered 
cases, and conclude that the prophet is a true one, and that 
the coincidence is an example of cause and effect. 

This fallacy often assumes a dilemmatic form, and was in 
constant use among the ancient Greek logicians, when en- 
gaged in their disputative tournaments. A celebrated in- 
stance is the following, which endeavours to show, from the 
argument of necessity, that it is of no use to strive against 
any occurrence, fortunate or unfortunate. 

If I ought to exert myself to effect a certain event, this 

event either must take place or it must not ; 
If it must take place, my exertion is superfluous ; if it 
must not, my exertion is of no avail ; 

.'. On either alternative, my exertion is useless. 

Here, in the major premiss, it is assumed that for the 
event to take place necessarily, and for it not to do so, are all 
the cases possible. But this enumeration is imperfect, as the 
event taking place may depend upon my own exertions ; and 
therefore, the alternative member of the premiss should be, 
" This event must either take place through my own exer- 
tions, or through some other cause, or not at all." 

Occasionally, the answer to a dilemma is to ^' retort " it ; 
i.e., to propose one which shall be correlative and reciprocal. 
The best known of these cases is called the litigiosus. Sir 
William Hamilton's account is as follows : — " It relates to 
an action between Protagoras, the prince of the sophists, 
and Euathlus, a young man, his disciple. The disciple had 
covenanted to give his masiter a large sum to accomplish 
him as a legal rhetorician ; the one half of the sum was 
paid down, and the other was to be paid on the day when 
Euathlus should plead and gain his first cause. But when 
the scholar, after the due course of preparatory instruction, 
was not in the same hurry to commence pleader, as the master 
to obtain the remainder of his fee, Protagoras brought 
Euathlus into court, and addressed his opponent in the fol- 
lowing reasoning : — ^ Learn, most foolish of young men, that 
however matters may turn up (whether the decision to-day 
be in your favour or against vou), pay me my demand you 



106 OF FALLACIES. 

must. For, if the judgment be against you, I shall obtain 
the fee by decree of the court, and if in your favour, I shall 
obtain it in terms of the compact, by which it became due 
on the very day you gained your first cause. You thus 
must fail, either by judgment or by stipulation.' To this 
Euathlus rejoined : — ' Most sapient of masters, learn from 
your own argument, that whatever may be the finding of the 
court, absolved I must be, from any claim by you. For, if 
the decision be favourable, I pay nothing by the sentence of 
the judges, but if unfavourable, I pay nothing in virtue of 
the compact, because, though pleading, I shall not have 
gained my cause.' * The judges,' says Gellius, ' unable to 
find a ratio decidendi^ adjourned the case to an indefinite day, 
and ultimately left it undetermined.' '* 

The *^ horned" dilemma is also a much-renowned fallacy. 
It consists of the question, "■ Have you cast your horns ? " to 
which, if you answer " No," I reply, " Then you have them 
still :" if you answer " Yes," I reply, "Then you have had 
horns." The error here is the assumption that you must 
either have had horns and cast them, or have had them 
and retained them ; whereas, another case is possible, viz., 
the fact that you have never had them. 

Another example is the fallacy of coiitinuous questioning, 
to which the name of sorites is often applied. It is thus em- 
ployed : — The sophist asks whether a man with so many 
thousand hairs on his head is bald. Y^ou answer, " No ; " 
and are next asked whether if he had one hair less he would 
be bald. The same reply being given, a further diminution 
of one hair takes place, and so on, until you are either forced 
to admit that you cannot distinguish between bald and not- 
bald, or that they differ by a single hair. The reasoning is 
based upon the supposition that a man must either be bald 
or not-bald, whereas he may be both : and this refutation 
does not involve a contradiction in terms, as at first it would 
seem to do, for " bald " and " not-bald " being relative terms, 
may, when their correlatives differ, be both applied to the 
same object. Of course, an exact method of evading the 
sophism would be to regard " bald " as meaning entire desti- 
tution of hair ; in which case there would be no absurdity in 



OF FALLACIES. 107 

maintaining that a single hair constituted the difference be- 
tween bald and not-bald. 

These will serve as a specimen of the fallacies invented by 
the Greeks for purposes of recreation. We ^vill now consider 
the practical forms in which false generalisation appears 
among the ordinary reasoning processes of philosophy and 
common life. 

The non causa pro causa is an error of very wide extent, 
and consists in imagining a causal relation between two facts 
which happen to occur either at the same time, or within 
some short interval of one another. Thus, the ancients 
imagined that anything which apparently moved of itself 
was animated, since they had observed voluntary motion to be 
accompanied by life in many cases : accordingly, they assumed 
that the stars were animated. Here, from observing a co- 
incidence, they inferred a causal relation, and so laid down a 
general law^ which, false in itself, was the parent of many 
kindred errors when applied to scientific speculations. So, 
too, from the fact that wars or pestilences have happened 
soon after the appearance of a comet, it has been held that 
heavenly bodies of like description are the causes, or at least 
precursors of great calamity. In this case, a sequence was 
considered as a relation of antecedent and consequent ; the 
technical name for such a fallacy being post hoc, ergo propter 
hoc, while the former is called cum hoc, ergo propter hoc. 

It is not, however, to be supposed that all examples of this 
fallacy are of such a simple description. Thus, a country is 
often said to be prosperous because it is rich, whereas in fact, 
it is rich because it is prosperous : or the government and 
constitution must be praiseworthy, because under them the 
country has flourished, the truth being that it has flourished 
in spite of them. 

The want of sufficient investigation frequently leads to 
false generalisation : iron, for instance, was supposed to be 
rusted whenever it came into contact w^ith water ; recent ex- 
periments have, however, determined that air, and probably 
carbonic acid, are also necessary to the production of this 
effect. Oxygen, as is imported by its name, was considered 
t..e active principle of all acids, merely because it was a 



108 OF FALLACIES. 

constituent of sucli as were then known analytically : the 
doctrine was but short-lived, owing to the discovery that many 
acids contained no oxygen whatever. And this will always 
be the case, where efforts are alone directed to discover the 
points of similarity between various bodies, instead of the 
attempt being made to ascertain the properties wherein they 
differ. 

" Experience '* has also much to account for as an erroneous 
guide : no public vehicle had been made to run at more than 
ten or twelve miles the hour ; therefore, to travel quicker by 
railway could never take place. A certain law has hitherto 
worked well ; therefore, it will never require alteration : the 
swans that had been seen before the discovery of Australia 
were white ; therefore, there were no black ones. No person 
had met with birds without wings ; consequently, until the 
apteryx was found in New Zealand, the notion obtained that 
all birds were thus provided ; and so on, the love of dogma- 
tising from truths within our observation to facts beyond it, 
being irresistible. ^ 

Of a similar nature is the employment of general pro- 
positions as such, which are only the result of a majority of 
cases : estimates of national character, for instance, when ap- 
plied to an individual case, cannot give a correct inference, 
although, of course, the conclusion may possibly be true. 
When I say the Hindoos are Pagans, I mean only that most 
of them are so ; and, therefore, were I to declare that this 
man is a Pagan because he is a Hindoo, my syllogism would 
either be invalid, the middle being undistributed, or the major 
premiss would be unduly assumed. 

5^. Fallacies from a False Estimation of ProhahiUties. 
A premiss which in itself is only probable, is not uncom- 
monly assumed as certain ; or, should it be just possible, it is 
taken as probable. The degrees of probability are also un- 
duly increased in many arguments, more especially where 
the reasoning takes the form of a sorites or epicheirema. 
Thus, if we were to argue that since earthquakes are possibly 
caused by sudden formations of steam within the earth, and 
since the intrusion of fused rocks and other highly heated 
matter into cavities filled with water would probably occasion 



OF FALLACIES. 109 

t 

such bursts of steam, therefore, the probable existence of in- 
ternal lakes may be inferred, we should vastly over-estimate 
the chances involved. So, *^ one of the great fallacies of 
evidence is the disposition to dwell on the actual possibility 
of its being false ; a possibility which must exist when it is 
not demonstrative. Counsel can bewilder juries in this way 
until they almost doubt their own senses. A man is shot, 
and another man, with a recently discharged pistol in his 
hand, is found hiding within fifty yards of the spot, and ten 
minutes of the time. It does not follow that the man so found 
committed the murder ; and cases have happened, in which 
it has turned out that a person convicted upon evidence as 
strong as the above, has been afterwards found to be inno- 
cent. An astute defender makes these cases his prominent 
ones ; he omits to mention that it is not one in a thousand 
against whom such evidence exists, except when guilty." * 

The chance of deception in such cases must depend, in a 
great measure, upon the capacity of the parties to decide 
upon the proper weight to be given to each probabiHty. If 
numerical values can be assigned to the various statements, 
the conclusion is merely a matter of arithmetical computation, 
but it would seldom be feasible to obtain the consent of an 
opponent to such a course. Accordingly, the best plan is to 
require that each proposition shall be expressed in one of 
these forms — '* A is more likely than not, to be D," or, *' A 
is less likely than not, to be D : " it is a simple matter then 
to arrive at a satisfactory result. 

6°. Fallacy of Reasoning in a Circle, This fallacy arises 
whenever one of the premises is the same in sense with 
the conclusion, and it is scarcely necessary to point out that 
its unfairness consists in the fact of assuming as already 
proved {i.e. as a premiss) the very thing which you are 
about to prove, viz., the conclusion. An argument might, 
for example, be maintained in the following manner : — 
** Light is certainly material, for it adds to the weight of any 
body which absorbs it, although in so slight a degree as to 
escape perception by our most exact means of investigation. 

* De Morgan's *' Formal Logic," pp. 275-6. 



110 OF FALLAGfES. 

And that it does so add to the weight results from the con- 
siderations that all matter is ponderable to some extent at 
least, and that when any substance is absorbed by another, 
the ponderosity of the former is necessarily added to that of 
the latter." If this train of reasoning were extended by a 
judicious introduction of illustrative examples of each state- 
ment, with elaborate analyses of the various principles in- 
volved, it might very possibly escape the observation of many 
readers, that to mention in such connection the case of one 
substance being absorbed by another, is, in reality, to assume 
the conclusion, t.e., that light is material. 

7*^. Petitio Principn is a modification of the foregoing, 
and occurs when the faulty premiss is "proved from the 
conclusion, or is such as the persons you are addressing are 
not likely to know, or to admit, except as an inference from 
it, as e.g., if any one should infer the authenticity of a certain 
history, from its recording such and such facts, the reality 
of which rests on the evidence of that history." ^ 

This fallacy is more dangerous than that of reasoning in a 
circle, from the circumstance that the premiss merely depends 
upon, and does not explicitly state the conclusion ; conse- 
quently, it often requires a minute and searching investiga- 
tion to detect the error. Hence, we cannot be surprised upon 
discovering" that many philosophers whose acuteness and 
intellectual power stand almost unrivalled, have yet fallen 
into the snare of petitio principii, or, in other words, have 
'^ begged the question " at issue. ** Plato, in the '* Sophistes," 
attempts to prove that things may exist which are incorporeal 
by the argument that justice and wisdom are incorporeal, and 
justice and wisdom must be something. Here, if by some- 
thing be meant, as Plato did in fact mean, a thing capable of 
existing in and by itself, and not as a quality of some other 
thing, he begs the question in asserting that justice and 
wisdom must be something.^' f 

It has, indeed, been urged that every syllogism is a case 
of the petitio principii, since the truth of the major premiss 

* Whately's " Logic," book iii. § 13. 
f Mill's " Logic/' book v. chap, vii. § 2. 



OF FALLACIES. 111. 

depends upon the truth of the conclusion. Thus, in this 
argument — 

All horses are quadrupedal, 
Bucephalus is a horse ; 
.'. Bucephalus is quadrupedal : — 
it is objected that before we can assert all horses to be 
quadrupedal, it must be true that Bucephalus is so. To dis- 
cuss the question involved would here, however, be out of 
place ; but those students who may wish for any further in- 
formation upon the subject will find such in the Appendix, 
Article D. 

A common method of expressing the petitio jprincijpn is to 
employ words, which, although synonymous, are yet of dif- 
ferent etymology and derivation. A happily -chosen example 
is thus given by Archbishop Whately : *^ To allow every 
man an unbounded freedom of speech must always be, on the 
whole, advantageous to the state ; for it is highly conducive 
to the interests of the community, that each individual should 
enjoy a liberty perfectly unlimited, of expressing his senti- 
ments." 

The remedy for the last-mentioned fiillacies consists in 
cutting down the chains of reasoning as much as possible, so 
as to bring the erroneous premiss and the conclusion into 
close juxtaposition, when it will not be a matter of any difficulty 
to discern their relation and inter-dependence. 

§ 6. Material Fallacies, Ignoratio Elenchi, 

1°. Argumenta ad Jiominerrij Sc. The passions and pre- 
judices of men having an enormous influence over their 
reasoning powers, a skilful sophist will often, by appealing 
to some particular bias, convince his hearers that such and 
such a proposition is perfectly correct, and then maintain that 
being so it must be received as universally true. Now, in 
doing this he has merely proved the conclusion partially, 
*.e., in so far only as his hearers are concerned ; whereas 
he should have proved it generally, and as applicable to all 
classes. Accordingly, he is guilty of an ignorance or evasion 
of the required proof {elenchus), this being the distinguish- 



112 OP FALLACIES, 

ing characteristic of the class of errors at present under 
examination. 

There are three principal heads contained under the first 
division of this class, viz., the Argumentum ad hominem, the 
Argumentum ad verecundiam, and the Argumentum ad popu- 
lum. Of these, the first consists in unfairly appealing to the 
opinions, &c., of the individual addressed ; the second, in 
similarly addressing the reverence entertained for old institu- 
tions and the like ; the third, in apparently determining the 
question by exciting the passions and fancies of the populace. 
Thus, I might go to one man whom I knew to be a disbeliever 
in the results of geological science, and compel him to admit 
that coal could not have required vast ages for its production, 
by arguing that the world itself had only existed for six 
thousand years ; this would be an appeal ad Jiominem. Again, 
I might go to another, and succeed in establishing the same 
conviction, by reminding him that surely he would never 
think of setting his opinion up against what had been main- 
tained by men of such learning and genius as so and so, and 
so and so ; here I should address my argument ad verecun- 
diam. Or, I might carry this point with a mob, by telling 
them that the contrary opinion was only upheld by those men 
who were always endeavouring to deceive the poor, and to 
take the bread out of the labourer's mouth by new-fangled 
inventions, which would be an argumentum ad populum. 

2°. Substituting a Part for the Whole, When a universal 
proposition cannot be established, it often gains admittance 
by the proof of its corresponding particulars. Thus, with 
regard to the various sciences it is frequently urged that none 
of the principles are trustworthy, because there has always 
been a difference of opinion as to facts and theory between 
even the most renowned philosophers. Here the assertion is 
true in a measure, for some facts and theories have undoubtedly 
given rise to continual discussion ; but, then, we must not lose 
sight of the fact that investigators of all parties and shades of 
opinion are in perfect agreement as regards the major portion 
of the respective sciences. And this form of ignoratio elenchi 
has a still commoner modification, viz., the assumption which 
persons frequently make, that upon their own preconceived 



OF FALLACIES. Il3 

opinions, naen of science are at variance, because controversy 
exists as to other doctrines; this being, not an inference of the 
whole from a part, but of one part from another. As might 
be expected from its recent development, the science of geo- 
logy is greatly exposed to these mistaken notions ; and in 
reference thereto, Sir Roderick Murchison has made the fol- 
lowing valuable observations: — ^'In all the grand leading data 
on which the history of geology is based, we [himself and 
Sir C. Lyell] are completeli/ united; whether it be in record- 
ing the regular succession of formations from the oldest to 
the youngest, the progression from lower to higher types of 
life, the enormously long periods which mnst have elapsed in 
the formation of deposits, and their frequent change into 
crystalline conditions by that metamorphism which he has so 
skilfully expounded ; or, lastly, in the evidences he has brought 
together to show that man must have coexisted with some of 
the great fossil mammalia. On all these subjects I hold the 
same opinions as himself; and I have ventured to make this 
explanation because it seems to me essential that the pablic 
should not run away with the idea that because geologists occa- 
sionaUi/ disagree on points of tlieori/ ,tliat there exists among them 
any divergence of opinion as to the great foundation stones 
on which their science has been reared.'' 

In the refutation of an argument we frequently meet 
with examples of this fallacy : the objector shows that his 
opponent is mistaken upon one point, and thence concludes 
that the whole of his reasoning is unsound even though it 
may in nowise depend upon the erroneous statement. ''Hence 
the danger of ever advancing more than can be well jiiain- 
tained, since the refutation of that will often quash the whole. 
.... Thus, also, a guilty person may often escape by having 
too much laid to his charge ; so he may also, by having too 
much evidence against him, i.e., some that is not in itself 
satisfactory. Accordingly, a prisoner may sometimes obtain 
acquittal by showing that one of the witnesses against him 
is an infamous informer and spy ; though, perhaps, if that part 
of the evidence had been omitted, the rest would have been 
sufficient for conviction." * 

* Whately's " Logic," book hi. § 18. 



114: OF FALLACIES. 

There may often be a combination of the ignoratio elenchi 
with other kinds of fallacies. Thus, instead of proving the 
impossibility of space being finite, philosophers are accus- 
tomed to prove its inconceivabiliti/ ; and the same thing occurs 
with regard to any limit of duration : both of these errors 
arising from the a priori belief that the conclusion proved, 
and the conclusion required, were in each case of equivalent 
import. So, too, if a supposed cause can be shown as suffi- 
cient to produce a certain effect, its existence is inferred, 
w^hen the real question is, have we any grounds to warrant the 
supposition itself. Until, for example, Torricelli had suc- 
ceeded in producing the vacuum to which his name is given, 
men of science were all agreed upon the statement that 
*^ Nature abhors a vacuum," a supposition which was suffi- 
cient to account for the difficulty they experienced in making 
a void space. The illustrious Newton himself adopted the 
opinion that an interstellar ether existed, not on account of 
those facts which have led modern philosophers to the same 
belief, such as the variation observable in the course of comets, 
and similar reasons ; but because he conceived that the effects 
of gravity might be explained by such an assumption. In 
the same manner he was obliged to suppose various arbitrary 
properties of different kinds of matter, in order that his pre- 
conceived theory of light should be accordant with the 
respective phenomena of colour ; but yet it must not be ima- 
gined that hypotheses are not often of very great service in 
scientific investigations ; for when cautiously applied, and 
only admitted as provisional, until a more extended know- 
ledge^ is attained, they form a most valuable instrument of 
reflection and observation. That such is the case will be at 
once apparent upon a mere mention of the atomic theory, 
which found chemistry a scattered, disjointed collection of 
isolated facts, and gathering the members into one organic 
w^hole, left it endowed with vitality, self-impulsive, and pos- 
sessed of unfathomable power. 

The fallacy of " shifting ground " should properly be ranked 
under this head, and occurs whenever a fresh point is raised 
before the former one is decided. This is also called " beating 
about the bush ; " it chiefly happens in conversational arga- 



OF FALLACIES. 115 

ments, and some very good examples may be found in the 
*' Dialogues '' of Plato. For instance, in the following passage 
from the ^' Gorgias " an ignoratio elenchi is finely exposed by 
Socrates ; the question being what name should be applied 
to Gorgias, the famous orator of Leontium : — 

ChcE. But now, since he is skilled in a certain art, what can we pro- 
perly call him ? 

Pol. Chaerephon, there are many arts among men by experience expe- 
rimentally discovered ; for experience causes our life to proceed according 
to art, but inexperience according to chance. Of each of these, different 
persons partake of different arts in different manners ; but the best of the 
best ; in the number of whom is Gorgias here, who possesses the finest of 
the arts. 

Soc. Polus appears, Gorgias, to be veiy well prepared for speaking ; 
but he does not do what he promised Chaerephon. 

Gor. How so, Socrates ? 

Soc, He does not appear to me to answer the question that was asked. 

Gor. Do you, then, if you please, ask him. 

Soc. No, but if yourself would be willing to answer me, I would much 
rather ask you. For it is evident to me that Polus, from what he has 
said, has studied more what is called rhetoric than conversation. 

Gor. Why so, Socrates ? 

Soc. Because, Polus, when Chserephion asked you in what art Gor- 
gias was skilled, you praised his art as if some one had blamed it, but 
you did not say what the art itself is. 

In all these cases the only plan of arriving at a satisfactory 
result is to come to a distinct understanding with regard to 
the question under debate : and if every proposition admitted 
or proved be closely compared with the conclusion required, 
it will be found that very little danger exists of sophistry 
proving successful. 

§ 7. Conclusion. 

Here, then, terminates our investigation of the several 
fallacies which most frequently occur ; and by a careful study 
of their various natures, together with the import of the rules 
laid down for their treatment, we shall find ourselves in a 
great measure secure against the common forms of error at 
least; but it will easily be understood that much depends 



116 OF FALLACIES. 

upon the extent of individual ability, for however perfect an 
instrument may be, it yet requires a directing intelligence in 
order to perform its work, and the more ably it is guided 
the better it will act. Logic can offer no panacea against 
the spread of deception. 

The preceding analysis has then enabled us, as far as rules 
go, to discover whether a given argument be fallacious or 
the reverse. Accordingly, we are now in a position to under- 
stand what true reasoning is, since we know what it is not ; 
and we may proceed with some certainty to the considera- 
tion of the various processes which are employed in the dis- 
covery of truth. In speaking of these processes, I of course 
allude to those operations which form the especial province of 
Logic, for although the formal laws of thought must be 
obeyed in every possible case of observation and reflection, 
yet there are certain actions of the mind in which they are 
more particularly concerned. These will form the subject of 
our next chapter. 



117 



CHAPTER VI. 

OF LOGIC AS PRACTICALLY APPLIED. 

§ 1. Introdiictori/ Remarks. 

The object of all science is the acquisition of truth, a subject 
which has as yet occupied but little of our attention ; indeed, 
it would have been impossible to have arrived at any accu- 
rate results respecting the laws of thinking, if we had not 
abstracted from these the matter upon which they operate. 
Now, however, that we have obtaired, as I trust, clear and 
accurate notions of the mode in which the natural constitu- 
tion of our minds influences the operation of all thought, we 
shall be quite prepared to investigate the results of such in- 
fluence, and to ascertain its practical effects. To do this suc- 
cessfully we must continually bear in mind the various prin- 
ciples which have been enounced during our survey of formal 
Logic : these relate to the three processes of apprehension, 
judgment, and inference, teaching us — first, that our objects of 
thought must be either the ideas of individuals or of classes ; 
secondly, that any assertion concerning these ideas must take 
the form of a quantitative comparison ; and, thirdly, that no 
reasoning is correct which does not conform to the syllogistic 
rules, which are proximate applications of the inherent mental 
canon. But the most transcendent product of our researches 
has been the firm establishment of the fact that the greatest 
instrument by which the mind works is si/ stem; it invariably 
strives to arrange the facts which it gathers, and to erect 
them into some connected structure ; the peculiar office of 
Logic as a science being to secure the symmetrical adjust- 
ment of parts which compose the fabric. This truth, I make 
bold to say, is the indispensable key to a proper understand- 



118 OF LOGIC AS PRACTICALLY APPLIED. 

ing of tlie nature and working of the reflective faculties : it 
may be seen to underlie each separate step of our inquiries 
hitherto ; and no explanation of the mysteries involved in the 
mind's search after truth can be complete unless it enters as 
an essential element. 

Thus much premised, it will readily be imagined that un- 
less our researches conform strictly to the natural laws of the 
intellect, we can only arrive at confusion and contradiction, 
instead of at truth ; for, although we must always in some 
degree be regulated by the inherent forms of thinking, yet in 
many cases a considerable deviation takes place, in conse- 
quence of an imperfect acquaintance with, and analysis of 
the principles which should be universally prevalent. This it 
is which occasions the necessity for an applied Logic ; that 
is to say, a science which shall point out the proper method 
of interweaving the laws developed by formal Logic, with 
the v/eb of facts that constantly come under our notice, in 
such a manner that we may attain to the most perfect and 
correct knowledge of them. And hence it will be apparent 
that in so doing these laws will require various modifications, 
in order that they may be accommodated to the respective 
circumstances of the case ; for it must not be forgotten that 
in treating upon the formal aspect of thought no account was 
taken of the phases into which reflection would fall when 
concerned with the truth and falsity of propositions. So, too, 
with the mathematical sciences ; the principles involved are 
analysed upon a partial consideration only of the facts to 
which they are ultimately applied. In geometry, for instance, 
points are regarded as possessing no magnitude, lines as 
without breadth, circles as perfectly uniform ; although for 
any practical purposes we must always make allowance for 
the many departures from theoretical supposition, which 
must invariably occur. And, paradoxical as it may seem, it 
is this very disregard of actual truth which confers upon 
mathematics and Logic the rigid exactness attending all their 
investigations ; the reason being, that by removing all dis- 
turbing influences, the attention is concentrated upon such 
points alone as are of vital importance to the laws which 
regulate the existence of the science. 



OF LOGIC AS PRACTICALLY APPLIED. 119 

Accordingly, we shall find that there is not that precise 
distinction between the several branches of applied Logic 
which we found to exist in the subjects about which formal 
Logic is conversant. The operations run, as it w^ere, hand 
in hand, presenting such an appearance of simultaneity, that 
it is often a matter of considerable difficulty to ascertain the 
exact nature of their mutual dependence and relation. They 
may, however, be grouped under two heads. Observation and 
Reflection ; the first of these being amenable to the laws of 
conception and judgment ; the second, to those of inference ; 
while connecting them is the motive power of classification, 
concerning which I have so often spoken. At the same time, 
it will be impossible, within the present limits, to do more than 
indicate the best method of studying the, vast subject of 
applied Logic ; which, comprehending as it does, the generic 
features of all the sciences existent and to come, has required 
the combined efforts of the world's greatest philosophers to 
attain its present development ; and which gives such promise 
of future progress as to warrant our most sanguine anticipa- 
tions of results which shall excel by far all that has hitherto 
been accomplished. 

§ 2. Observation, 

The process of observation naturally presents itself before 
us as having the prior claim upon our attention ; for it is 
evident that it must always precede reflection, as without 
objects to think about there would be no thought. And 
here it behoves us to determine more expHcitly than hereto- 
fore the import which attaches to the phrase '' objects of 
thought ;" as otherwise some ambiguity of expression would 
be likely to occur in consequence of the idea generally attached 
to the word " object." This, in ordinary parlance, is held to 
imply some substance or existence which produces an impres- 
sion upon our minds, but, when used philosophically, may also 
signify the impression itself. If, for instance, I say, " Heat 
is a most mysterious thing," I may either mean the sensation 
of heat, or the cause of that sensation ; and it is with words 
of this description that confusion commonly arises. Thus, in 
Mr. Mill's elaborate and masterly ^' System of Logic," from 



120 OF LOGIC AS PRACTICALLY APPLIED. 

"whicli I have often had occasion to quote, there is the follow- 
ing passage : ^' But from these and similar generalisations 
countenance and currency have been given to attempts to 
resolve, not motion into motion, but heat into motion, light 
into motion, sensation itself into motion;" where **heat" and 
*4ight" would appear to mean the outward causes of the respec- 
tive sensations, and not the sensations themselves ; for other- 
wise there needs to be no distinction drawn between " heat," 
"light," and *' sensation; but yet, a few lines further on, we 
read, " All I insist upon ... is, that it shall not be supposed 
that by proving these things [i.e., *' that certain motions in 
the particles of bodies are among the conditions of the pro- 
duction of heat or light "] one step would be made towards 
a real explanation of heat, light, or sensation. . . . Let it be 
shown, for instance, that the most complex series of physical 
causes and effects succeed one another in the eye and in the 
brain to produce a sensation of colour ; . . . still, at the end 
of these motions, there is something which is not motion, 
there is a feeling or sensation of colour." Here, indisputably, 
Mr. Mill is combating the supposition that the sensation of 
heat, light, &c., is motion, a proceeding, however, altogether 
irrelevant to the question in hand (as at first stated), viz., 
whether motion is the cause (or " among the conditions ") of 
such sensations. An example of this nature is the more in- 
structive, as it will be easily supposed that when so acute 
and profound a philosopher is led into a confusion of expression 
(for one cannot imagine that there is any confusion of thought) 
by the ambiguity above-mentioned, multitudes of inferior 
writers will continually mistake the point to be proved, and 
w^ill involve their arguments accordingly. 

Now the word " phenomena " would appear to be better 
adapted than any other for expressing the notion intended to 
be conveyed by the phrase ^'objects of thought;" it being 
seldom used but in a strictly philosophical sense. We shall, 
therefore, in the first place, ascertain the nature of those phe- 
nomena concerning which our thoughts are occupied, having 
in view the determination between such as are, and such as 
are not, the subjects of direct observation. 

Every phenomenon is either subjective or objective ; either 



OF LOGIC AS PRACTICALLY APPLIED. 121 

a condition or state of our mind, or a condition of sonoething 
apart from our mind. Any knowledge that we may possess 
of the former must obviously be the result of intuition or im- 
mediate perception ; but as regards the latter, the operation 
is by no means so simple, even in the most familiar and, appa- 
rently, incomplex cases. Thus, when I touch a piece of 
iron and say, '' This iron is hot," the train of thought from 
which the judgment results is of the following character : — 
I look in a certain direction, and am immediately impressed 
with those sensations of sight, which, from prior experience, I 
have concluded to be always produced by a series of pheno- 
mena termed *' iron." I extend my hand in the same 
direction, and receive two sets of sensations, one consisting of 
" hardness,*' &c., thus corroborating the evidence of my eyes 
as to the existence of '^ iron," and the other reminding me of 
sensations similar to those antecedently produced by cases of 
*' heat." I, therefore, feel certain that a series of phenomena 
exists before me, which resembles a large class of other series in 
its capacity of raising up a particular sensation, known by the 
name of '^ heat ; " a conviction which I express by saying, *' This 
iron is hot." Here, then, a process which w^ould be com- 
monly called an act of observation, is seen to consist of two 
steps: first, the perception of certain sensations, and secondly, 
an inference based upon the existence of these sensations : 
consequently, the truth of the statement must depend upon 
the correctness of the reasoning. Nor is this analysis by any 
means unimportant, for it frequently happens that a supposed, 
but non-existent, fact is taken for granted, merely because it 
has been observed; whereas the truth is that it was inferred. 
There is. for example, a beautiful experiment in optics, where 
a revolving wheel is rendered visible by means of flashes of 
light, so adjusted that the wheel is once illuminated during 
each revolution ; the effect of this being that although the 
wheel revolves at the rate of several hundred times a minute, 
it yet appears to be standing perfectly still ; and so perfect is 
the illusion, that even to imagine it as such is almost impos- 
sible. The explanation of this is, that the means employed 
in the experiment produce sensations which are indistinguish- 
able from those produced by a wheel standing perfectly still, 



122 OF LOGIC AS PRACTICALLY APPLIED. 

and this latter phenomenon we accordingly infer to be the 
case ; an instance of fallacious a priori reasoning, where the 
supposition that an effect has but one cause is unduly assumed. 

Accordingly, we find that the only phenomena which can 
be the subject of direct observation, and concerning which 
we may arrive at truth by means of direct observation, are 
subjective ; that is to say, the existence of certain sensations is 
the only thing of which we can be sure when the observing 
faculties are alone employed. At the same time, it would 
serve no useful end if we were to push this doctrine to its 
extreme limits, and more especially in a treatise like the 
present, which cannot enter very minutely into the ultimate 
})rocesses of thought ; suffice it, therefore, to have called the 
attention of the student to a point so interesting and essential, 
as by so doing it may be reasonably hoped that he will have 
been put sufficiently on his guard to prevent any chance of 
error arising from this cause. In future, then, I shall not 
care to be rigidly precise when making use of expressions 
which involve the process of observation ; but I shall still 
hope to be philosophically exact, for, as we formerly saw when 
treating upon the parallel case of the so-called immediate 
reasoning compared with syllogistic inference, a preliminary 
examination and subsequent neglect of some mental operations 
is by no means incompatible with a correct exposition of 
logical science. 

Assuming, then, that a comparatively loose sense may be 
attached to the notion of observation, we have next to inquire 
into the nature of the process as logically required for the 
purposes of science ; and, as science is merely concerned with 
the acquirement of truth, it follows that the end of logical ob- 
servation should be the formation of correct conceptions with 
reference to those phenomena which are the objects of thought. 

Now, the first requisite is that our notions should be clear ; 
that is to say, that they should be determinedly fixed; and 
as the method of arriving at general conceptions, or, in other 
words, the process of abstraction, has already been described 
as regards its formal aspect, it now remains to introduce the 
element of material truth. The main feature of the process 
consists in comparing together a number of individual objects 



OF LOGIC AS PRACTICALLY APPLIED. 123 

with a view to ascertain tlieir points of resemblance, and 
then conceiving a class composed of any number of objects 
which might happen to possess those points ; and this dupli- 
cate operation can only be correctly performed by attending to 
the following considerations. Let us endeavour, for example, 
to trace the formation of the conception " metals." We 
meet with certain individual objects, say gold, silver, and tin, 
and we wish to obtain such a general notion as may enable 
us to remember ihe sensations produced equally by each one 
of them, and by no other thing. We accordingly analyse 
the complex impression of each individual, i.e., we concen- 
trate our attention successively upon each separate one of the 
sensations, and note those which were produced indifferently 
by gold, silver, or tin. Extending our language a httle, we 
may describe ourselves w^hen so doing as observing the attri- 
butes which were possessed in common by the three objects, 
gold, silver, and tin. Suppose us, therefore, to remark that 
they all possess weight and hardness ; we might here pause 
and give the name of *' metal" to the combination of those 
two attributes, but were we to do so, we should find that such 
an idea was not complex enough to distinguish gold, silver, 
and tin from many other objects, such as stone, wood, &c. ; 
that is to say, we should not have formed a clear and distinct 
idea of a metal. We, consequently, resort to observation 
again and again, until we have abstracted such a combination 
of attributes, that gold, silver, and tin are the only objects 
which we know to possess it ; we can then clearly recall the 
sensations produced by a '' metal." This capability, however, 
would only belong to ourselves, who had performed the above 
process ; and were we to employ the name in communicating 
w'ith other persons, it would be necessary for us, in the first 
place, to define exactly w^hat we mean by the term, as other- 
wise they might attach a different signification to it, and 
might include the notions of things totally different from gold, 
silver, and tin. Here, then, we have two sources of obscurity, 
imperfect abstraction, and imperfect definition ; the remedy 
for the former being renewed observation ; for the latter, those 
rules which were laid down when treating upon definition in 
the second chapter of this work, 

g2 



124 OF LOGIC AS PRACTICALLY APPLIED. 

The second requisite for correct conception is that our 
notions should be appropriate ^ that is to say, that they should 
have a proper relation to the question in hand. There can, 
of course, be no general rule laid down as to what this rela- 
tion must be in every case, for that can only be settled by 
the specific end which we propose to ourselves ; but yet it 
may be remarked that the attributes observed should all have 
some distinct reference to the principle of division adopted in 
the particular science under investigation. Thus, in the ex- 
ample chosen above, our notion of '* metal " would include 
such marks as hardness, weight, ductility, and malleability, if 
we were occupied with mechanical researches ; to these would 
be added the capability of forming a base by union with 
oxygen, if chemistry were our object ; while the study of 
physics would necessitate the inclusion of '* great conductive 
powers" among the metallic attributes. 

If, therefore, we take care that our conceptions are clear 
and appropriate, ascertaining at the same time that our senses 
do not deceive us as to the real existence of the properties 
observed, wq shall so far be in the possession of truth, and our 
consequent reflections will rest upon a sound basis. This is 
all that can be done by observation, and as the nature, con- 
ditions, and end of this process have now been described, it 
would appear that nothing further remains to be added : 
before, however, I quit this portion of my subject, it may be 
advisable to offer a few remarks upon the mode of observing. 

We have already seen that, strictly speaking, subjective 
facts only can be directly observed ; but that no inaccuracy 
need result if we admit the application of the process to cer- 
tain objective phenomena. It is these latter which wall now 
be considered. And, first, we must note that observation 
may be direct or indirect ; that is to say, we may either 
employ our unaided senses, or we may make use of instru- 
ments to assist us. In the former case, the chief truths at 
which we arrive are those of quality; in the latter, of quantity. 
Thus, by making use of the eye alone, we can form an approx- 
imate notion as regards the height of an object, and this will 
be nearer to the truth according as our practical experience 
is greater; but to know it exactly, we must employ some 



OF LOGIC AS PRACTICALLY APPLIED. i-O 

measure. Here, in one case, we could merely be sure that 
the object possessed some height ; in the other, we could tell 
the exact amoimt. Or again, a ray of light appears to ordi- 
nary observation as perfectly homogeneous and white; Saturn, 
too, is a mere luminous point ; but the application of a prism 
reveals the existence of various colours in the sunbeam, while 
a telescope discloses the vision of a far-off world encircled 
with a glittering belt ; and with the perfection of the instru- 
ment Sidvsinces, pa7'i passu f our powers of observation. In the 
solar spectrum, for instance, Fraunhofer was just able to 
ascertain the duplex nature of the line D, but, recently, 
M. Gassiot, with his magnificent spectroscope, has resolved 
it into at least sixteen distinctly defined lines. And the same 
thing took place with regard to Saturn ; the employment of 
a higher telescopic power showed that what at first seemed 
to be but one belt, was in reality two. It will thus be seen 
that when the capability of exact admeasurement by means 
of instruments is asserted, all that can be strictly understood 
is our power of fixing definite limits in one direction at least ; 
and hence we gather that the best method of forming correct 
conceptions is by observing as precisely as possible, both the 
nature and amount of the properties wherein bodies resemble 
or differ from each other. We must, however, bear in mind 
the fact that although two attributes differ very much in 
quantity, yet, if they are alike in quality/, they will produce 
exactly the same kind of sensation, although varying in degree ; 
consequently, we must place them together in the same class. 
In our example of '' metals," gold, silver, and tin all possess 
the mark of ^' weight," but in very different quantities, this 
difference being one of their distinguishing characters as 
individuals ; and, therefore, if we were to meet with some 
other object, such as lead, and were to recognise in it the 
existence of the same kind of attributes as those which we 
abstracted from gold, silver, and tin, to constitute the notion 
of a metal, we should at once refer it to that class, although 
each mark might present a totally different appearance as 
regarded its amount. 

Experiment may also be considered as an act of observa- 
tion ; for although usually the result of reflection, yet in itself 



126 OF LOGIC AS PRACTICALLY APPLIED. 

it differs not from the ascertainment of attributes or properties 
by means of an instrument. In the present place, therefore, 
we shall merely consider it from the latter point of view, and 
shall defer all inquiry into the motives for its performance 
until we come to treat upon the processes of which it is a 
necessary accompaniment. A dear notion then can only be 
obtained from experiment, by closely observing the nature and 
anaount of the difference between the respective state of things 
before the commencement, and after the termination of the 
act ; while as to what is an appropriate notion, must be wholly 
determined by the particular object for which we performed 
the experiment. Thus, if I wished to ascertain the mechanical 
effects of heat upon red glass, I should notice that the latter 
became plastic when very hot ; but were I investigating 
its optical properties, I should confine my attention to the 
fact that its colour had changed from red to green. 

And here it may be remarked that Logic can no more 
make men good observers than she can make them good 
reasoners, except in so far as the adherence to rules laid 
down in strict accordance with mental laws will tend to a 
healthy exercise and invigorating discipline of the intellect. 
It is a just saying that " practice makes perfect," but all the 
watering and attendance possible will never produce an oak 
from a thistle-seed ; and so the most that can be done is to 
cultivate to the best advantage whatever has been originally 
implanted. Accordingly, the end of observation — i,e,, the 
attainment of correct notions — will be greatly promoted by 
the habitual exercise of the faculty in accordance with the sug- 
gestions given above ; but it is necessary that a good observer 
should also possess a retentive memory and wide experience, 
as otherwise his ideas would soon become confused, or they 
would not accord so closely with actual truth as to be of much 
avail for practical purposes. 

§ 3. Reflection. 

1°. Of Laws and Causes, As yet our attention has been 
confined to the ascertainment of what amount of truth may 
be acquired by the employment of observation alone. We 



OF LOGIC AS PRACTICALLY APPLIED. 127 

have found that even when the widest latitude is allowed, 
the results so obtained are merely a collection of separate 
ideas, these ideas being composed of various resemblances 
and differences. But, numerous as such notions may be, they 
constitute a very small portion indeed of existent truth. 
We have certainly coasted along the shore, and surveyed its 
general features ; the vast interior, however, still remains un- 
explored. That is to say, having collected the facts, we must 
now examine into their connection, and in so doing we shall 
perceive that the laws of inference are alone adequate to the 
task : therefore, without a previous knowledge of them, our 
labours would but terminate in confusion and disappointment. 

The bare existence of phenomena has hitherto been the 
subject of our analysis ; we must now endeavour to justly 
appreciate the modes in which they exist ; and as the order 
of time is here alluded to, it will at once be seen that a list 
of these modes may be easily made ; in fact, there are but 
two — coexistence and sequence, for phenomena must either 
occur together, or in succession. Which order obtains in any 
particular case is, of course, determined by observation ; the 
right understanding of such order is the office of reflection. 

Xow, in our sphere of thought, we cannot but observe that 
a certain principle of uniformitj/ prevails, more or less, in 
every occurrence which comes under our notice. Thus, a 
heavy body if unsupported falls to the ground ; a pressure, 
when not sufficiently opposed, is followed by motion in the 
object pressed ; death invariably succeeds the infliction of 
certain wounds ; the explosion of gunpowder is always accom- 
panied by the extrication of heat and light. All these facts 
must impress themselves strongly upon our attention. But in 
other cases the uniformity is by no means so general ; it is 
only some men, for instance, who have black hair ; it is only 
occasionally that we meet with natural springs whose waters 
are more highly heated than the surrounding earth ; it is nofc 
always that a west wind is accompanied by rain. These con- 
siderations lead us to a distinction between uniformities, 
which we accordingly regard as necessary, or casual ; as 
invariably occurring, or happening, as it were, by chance. 
The grounds upon which this distinction may be correctly 



128 OF LOGIC AS PllACTICALLY APPLIED. 

made will shortly be explained ; at present we are concerned 
simply with the fact as it stands. 

The impression produced upon onr minds by the regula- 
rity with which many phenomena recur is that nature works 
according to some uniform necessity, this being termed a law ; 
and, consequently, we speak of certain uniformities as being 
laiDS of nature. Thus, we say that for matter to possess 
weight as one of its attributes is a natural law ; that the 
orderly constitution of nature renders it necessary for water 
to tend to find its level; that motion unopposed must con- 
tinue for ever. It is, however, only to truths of this ultimate 
description that the term "laws of nature" is appKed ; many 
uniformities which at first sight might appear of the same 
description, being in reality resulis of the former. Thus, 
that the moon should revolve about the earth as a centre, 
would, from the perfect uniformity of the revolution, seem to 
be a natural law; but closer investigation shows that the 
motion takes place in obedience to three separate laws applied 
under certain circumstances. In fact, w^e might predict a 
priori such an effect as resulting from given conditions, but 
we could not predict the conditions themselves antecedently 
to experience. 

And this leads us to a cognate consideration of great im- 
portance ; the determination of what is implied by the expres- 
sion ** resulting." Here, of course, the cases are limited to 
uniformities of sequence — that is to say, those phenomena 
which we always observe to occur in regular succession. The 
names usually applied to any duplicate set of this description 
are cause and effect; reference being made to a law of nature, 
which must now be explained, viz., the law of universal caus- 
ation. Some idea of the mode in which we arrive at this 
law may be thus given : we observe throughout nature that 
whenever anything occurs there have always existed some 
antecedent conditions ; and we also observe that certain con- 
ditions are invariably followed by definite consequents. If I 
feel unwell I know that some abnormal state of my body has 
previously supervened ; if I thrust my hand into the fire I 
know that sharp pain will immediately succeed ; w^hen rain 
falls we fee] certain that the suspension of water in the air 



OF LOGIC AS PRACTICALLY APPLIED. 129 

preceded the storm ; or, should we pass a strong current of 
electricity through a piece of thin platinum wire, we are 
assured that the latter will speedily become red-hot. Expe- 
rience of this nature leads us to the conclusion that if any- 
thing have a beginning it has also a came ; that is to say, 
some condition, or group of conditions, must have previously 
existed, in virtue of which existence the phenomenon in 
question was produced. 

But we must not suppose that all uniformities of sequence, 
how universal soever they may be, are cases in which the 
law of causation operates ; for it will have been observed that 
the name of cause is only applied to those conditions in virtue 
of whose existence the effect necessavilij follows — to those phe- 
nomena without which other phenomena would not occur, 
but which being once posited the other must spring into 
being. Therefore, when the sequence is merely casual, and 
there is no connection of necessity between the events, w^e 
cannot refer them to the law of causation : for example, 
when summer invariably follows spring ; autumn, summer ; 
and winter, autumn ; it could not be said that one season was 
the cause of the next, for then the two requisites of cause and 
effect would be violated ; it being possible for a perpetual 
summer to exist, or for winter to immediately succeed summer 
without the intervention of autumn, in consequence of some 
cluange taking place in the earth's position with regard to the 
sun, or in the present physical configuration of the earth. 

Nor must any mere arbitrary limit be placed upon the 
signification of '' cause ; *' we must not make a selection from 
the conditions upon which an event depends. It is true that 
this is almost invariably done, as when the prick of a needle 
is said to be the cause of the pain which I feel ; or when iron 
is said to be dissolved because sulphuric acid is poured on it ; 
or, again, when the metamorphism of certain rocks is said 
to be produced by the action of fire. In all these cases there 
is an omission of necessary particulars. Thus, in the first, 
I should not feel pain from the prick unless I w^ere alive, and 
possessed a certain organisation, &c. ; in the second, the iron 
W'ould not be dissolved if, in addition to the mere presence of 
the acid, ihere did not exist a certain attraction between 

g3 



130 OF LOGIC AS PRACTICALLY APPLIED. 

oxygen and iron, oxide of iron and sulphuric acid ; while in 
the third, some physical properties of matter, such as polarity, 
(fee, are equally essential with heat to the production of the 
effect. Also, in every case there must necessarily exist a 
negative condition, besides those which are positive; this 
being the absence of counteracting causes, that is, those con- 
ditions which tend to produce a contrary effect. Thus, in 
the present state of the solar system, the earth keeps at a cer- 
tain distance from the sun ; but were the latter body and his 
attendant planets in their common motion through space to 
enter some resisting medium, the earth, although acted upon 
by all its former influences, would yet fall into the sun by reason 
of the new condition preventing the old causes from producing 
their wonted effects. 

Accordingly, the vulgar sense of the word cause does not . 
express its philosophical import ; and this ambiguity it will 
be necessary to bear in mind, as, from the convenience attach- 
ing to limited notions, it is often expedient for the attainment 
of the purpose in hand to consider that the cause, which 
really is but a portion of the conditions requisite for the pro- 
duction of the effect. For instance, when heat is said to 
cause the expansion of a bar of iron, we mean that heat is 
the condition whose introduction amongst other conditions 
gives rise to the change in volume ; or, in the example given 
above, the resisting medium would be said to cause the earth's 
fall into the sun, not because it could produce such an effect 
when acting alone, but on account of its enabling gravitation 
to act under less opposition from centrifugal force. 

It will now be seen that a law of nature is nothing more 
nor less than the expression of the relation existing between 
any single cause and its effect. By applying this doctrine to 
the truths first cited as natural laws, we may obtain a clear 
notion of its application. That matter possesses weight, then, 
means that wherever the entity termed matter exists it will 
possess the attribute of weight ; but it may be said that 
matter would not be matter without possessing weight, and 
that, therefore, weight would be simultaneous in its existence 
with matter. This, of course, opens up the question as to 
all ca^es of cause and effect, for who can say that the conse- 



OF LOGIC AS PRACTICALLY APPLIED. 131 

quent does not commence to exist at the selfsame moment 
that its conditioning antecedents are complete ; so that the 
argument, if valid, would show that there is no such thing as 
sequence in any case of causation. Now I am very far from 
denying the cogency of such reasoning, but this I do say, that 
for all practical purposes we may safely admit the notion of 
succession. As, therefore, ^Sveight" is but the attraction 
subsisting between material bodies, w^e may assume that w^ere 
some new matter to be created it would have no weight until 
it attracted, and had been attracted by other matter ; this 
operation taking place by virtue of a natural law that renders 
its occurrence a matter of necessity. And so with the second 
and third lavrs ; whenever a gravitating fluid exists there 
results an equal pressure in all directions, this fact being ex- 
pressed by the statement that water tends to find its own level ; 
or, Instl}', whenever motion exists alone, it continues for ever. 
In all these cases the antecedents are the causes, the conse- 
quents are the effects, and the necessary connections between 
the respective pairs of phenomena are the lavvs. 

2°. Of Induction, When speaking of observation, I had 
occasion to remark, that the existence of objective facts was a 
matter of inference based upon our ** experience " of subjective 
phenomena ; and again, in the preceding division, we found 
that the distinction between necessary and casual uniformities, 
w^as also originated by the accumulations of observation, i.e., 
by " experience." What is the meaning of this phrase must 
now, therefore, be discussed. 

We have just synonymised ** experience" by the expression 
'^accumulation of observations;" but when w^e say that a 
certain proposition is warranted by experience, we do not 
mean that our inference rests upon the whole mass of observa- 
tions which we have ever made, but that a consideration of 
such observations as relate to the fact in question, has disposed 
ns to infer, as a general truth, the uniformit}' which constitutes 
the judgment. That is to say, by reflecting upon certain 
separate observations, we are induced to believe in the exist- 
ence of some law. The operation of the mind by which this 
result is produced, has been named Induction, and may be 
defined as the process of assigning causes for effects. 



1S2 OF LOGIC AS PRACTICALLY APPLIED. 

Now, as it is by induction that we arrive at laws and 
causes, which, as shown above, constitute by far the major 
portion of existent truth, it follows that in an exposition of 
applied Logic this operation of the mind must occupy the 
most important position. And, accordingly, it will be advisable 
to treat as fully as our limits of space will allow, upon the 
nature and method of correct induction ; or, in other words, 
upon the mental laws which impel us to generalise from 
experience, and upon the quantity and quality of that ex- 
perience, which these laws render necessary for the establish- 
ment of a correct inference. 

Let us, then, in the first place, retrace the steps by which 
we have arrived at any proposition, and endeavour to ascer- 
tain upon what fundamental ground they all rest. Suppose 
we take this judgment, '* The earth is a globe ;" the question 
then comes, what are the premises from which such a conclu- 
sion was derived ? These we know to be ** every body which 
in certain positions would cast such and such a shadow^ upon 
the moon, and w^hich could be circumnavigated, &c., is a 
globe " (U) for the major, and '^ the earth possesses these 
attributes " for a minor ; and as the latter is the direct pro- 
duct of observation (loosely), it remains to be considered how 
the former was obtained — that is to say, we must next 
examine our grounds for stating that all globes possess the 
properties in question. This judgment cannot, of course, be 
the direct product of observation, for even had we been able 
to examine every globe at present existing, the proposition 
directly resulting would not be equivalent to the one above 
stated, which, being universal, must apply to all globes which 
have ever existed, or will exist henceforth, in addition to 
those of present entity. It must, consequently, depend upon 
reflection, i.e., upon a process of reasoning from observed 
facts ; and as we have seen in formal Logic, that all reasoning 
whatever may be reduced to syllogisms, it results that the 
judgment, '' all globes possess such and such properties," is 
a conclusion drawn from previously established premises. Of 
these Observation gives one, viz., '* This, that, and the other 
globe, have been found to possess the attributes above men- 
tioned ;" and, therefore, since the syllogism is vaUd, the other 



OF LOGIC AS PRACTICALLY APPLIED. 133 

must be to tliis effect, " Whatever may be predicated of this, 
tliat, and the other globe, may be predicated of all globes ;" 
\Yhich means, *^ Whatever attributes are found to accompany' 
this, that, and the other globe, \Yill be found to equally accom- 
pany every other globe." Pursuing a similar course, we next 
arrive at the following syllogism : — 

A case of a certain particular uniformity is a case of the 

corresponding general uniformity, 
The case of this, that, and the other globe being found 

to possess the attributes in question, is such a case of 

particular uniformity ; 
.*. The case of this, that, and the other globe being found 

to possess certain attributes, is a case of all globes 

being similarly marked. 
Now beyond this we cannot go ; that is to say, we cannot 
assign any premises which would necessitate as a conclusion 
the last-mentioned major-premiss. Accordingly, for all pur- 
poses of Logic, we must assume the principle thus stated to 
be a fundamental law of the mind, by which, from ascertaining 
one truth, we are compelled to believe another. Its enuncia- 
tion in the above syllogism is manifestly of a very partial 
character, as a due comprehension of its import would neces- 
sitate a complete explication of the phrase, ^'r certain particular 
uniformity ;" but this is the province of inductive method, and 
is foreign to our immediate purpose, viz., the treatment of 
inductive elements. To firmly establish these, we must next 
show that the law at which we have just arrived, is really of 
the nature claimed for it, i.e., fundamental. At the same 
time, it will not be necessary to proceed any furth'er with an 
investigation of the mind's ultimate constitution, as to do this 
would be to intrench upon the domain of metaphysics. But 
we must rather endeavour to show, that all other principles 
of reasoning, or axioms, are merely differentiations of tlie 
foregoing law. And as so wide a subject could not be 
entirely discussed in our limited space, it will be sufficient if 
we confine our attention to the axiomatic /* law of causation," 
and to any one of the mathematical principles ; say, ^* if equals 
be added to equals, the wholes are equal." 

We have already taken occasion to remark that the first of 



134: OF LOGIC AS PRACTICALLY APPLIED. 

these axioms is the result of experience, — that it is our 
observation of some cases of antecedence which induces us 
to believe that oM events are the effects of causes. But 
unless there existed some necessary mental law to legitimatize 
this inference, w^e should obviously be unable to rely upon its 
correctness, as then the only conclusion that could possibly 
be trustworthy, w^ould be that resulting from an inductive 
syllogism of the kind mentioned in Formal Logic ; in other 
words, we should be unable to proceed beyond the limits of 
our actual experience. Consequentl^T-, our observations of 
various instances of cause and effect require the aid of the 
inductive law before we can deduce any such general state- 
ment as that under consideration, and which is often termed 
'' the assertion of nature's uniformity." 

The second axiom, although usually considered funda- 
mental, is, strictly speaking, of more complex derivation than 
the law of causation ; for the latter is but one step removed 
from the inductive principle, while the former is separated by 
two syllogisms. These may be thus expressed : — 
1°. Certain particular uniformities legitimatize the inference 
of the corresponding general uniformities, 
Some cases of equal magnitudes being the same number 
of coincident magnitudes, constitute the required 
particular uniformity ; 
\ It is true that " all equal magnitudes are all coincident 
magnitudes." 
2"^. All equal magnitudes are coincident (U), 
All sums of equals are coincident ; 
.*. All sums of equals are equal. 

I h'ave stated the second argument as a simple syllogism, 
although it would be possible to show that it is of an epi- 
cheirematic nature, the minor premiss being a conclusion 
based upon the major. But this matters not in the present 
place, where we are only concerned with proving that the 
canon, '* if equals be added to equals, the wholes are equal :" 
or, as otherwise expressed, ^' the sums of equals are equal," 
is dependent for its adoption upon the inductive law, and has 
per se no locus standi. An inspection of the above reasoning 
will show that w^e have effected our purpose, and that the 



OF LOGIC AS PRACTICALLY APPLIED. 135 

fundamental grounds of the mathematical axioms are observa- 
tion conjoined with reflection ; the knowledge acquired by , 
experience being developed and increased by the laws which 
regulate our minds.* 

It will be remembered that when treating upon syllogistic 
inference, we found the fundamental law of that process to be 
directli/ inapplicable to many forms of reasoning, insomuch 
that for practical purposes it was developed into a series of 
proximate rules, which were sufficient to test the validity of 
all arguments, without our being at the trouble of effecting a 
reduction to syllogisms of the first figure. The same thing 
occurs in Applied Logic. We must differentiate the law of 
induction to such an extent, that the proximate canons thus 
obtained may enable us to judge correctly as to the truth of 
the propositions at which we arrive, and may render any 
reference to original principles unnecessary. But since such 
a differentiation can only be accompHshed by completely ap- 
preciating the meaning of the inductive law ; it follows that 
the doctrine of inductive method will next claim our attention. 

Now^, the truths at which we arrive by means of induction, 
are of two kinds : either the statement of general laws, 
i.e., an assertion of natural uniformities, without any exact 
discrimination of cause and effect, such as mathematical 
axioms, &c.; or the knowledge of special laws, which consists in 
the assignment of definite causes for definite effects, and vice 
versa, as, for instance, the truths of astronomy or chemistry. 
And, first, w^e will inquire as to what kind of experience 
warrants us in concluding the latter class of truths. 

The cause of any effect is, as already stated, the whole of 
the conditions which unite in producing it ; but this definition 
being too wide for my present purpose, I shall in the fol- 
lowing remarks understand by a cause " that circumstance 
w4iich produces some definite change in a set of antecedent 
conditions:" thus, a bell w^hile sounding remains in exactly 
the same state as when it was silent, with the exception that 
its particles are vibrating : this vibration, then, is termed the 



* Some additional exposition of this subject will be found in Ap- 
pendix D. 



136 OF LOGIC AS PRACTICALLY APPLIED. 

cause of the sound. So much being premised, I shall now 
investigate the mode in which we may determine the cause 
of any phenomenon. 

It will of course be evident, that the cause must exist 
amongst the conditions which compose the phenomenon in 
its totality ; for otherwise, there would not be that connection 
of necessity which we have seen is essential in every case of 
a sequence obeying a law. If, therefore, we have two or 
more instances of the effect which differ from each other in 
some things, but all agree in certain conditions, these latter 
are the only things which exist in every instance of the effect, 
and, accordingly, in them the cause must be sought. We 
thus obtain the canon of Agreement, which runs as follows : — 
1^. The cause will be found among the circumstances in 
which two or more instances of the effect agree. 
.Or, 
A uniformity which is observed in two or more instances, 
may be considered as invariable and necessary. 
If, for example, we found that gold and silver both con- 
ducted heat, we might say that the cause of such a power 
was included in the possession of metallic attributes, since 
that would be the sole circumstance in which the instances 
agreed ; or, in accordance with the above variation of the 
canon, it would be allowable to hold that every metal is 
capable of conducting heat. We can, however, only infer 
absolute laws, whether the observed effects be relative or 
absolute ; thus, from gold and silver being heavier than 
water, we cannot conclude that all metals are so, as the phe- 
nomenon investigated was not precisely the same in each 
case, i.e., the two metals differed in the amount by which 
they were heavier than water. But since they definitely 
agreed in possessing weight, we may affirm that property of 
all metals ; indeed, it forms one of the purely metallic 
attributes. 

The information acquired by means of the above canon is 
seldom satisfactory, as we are only able to ascertain the pre- 
cise cause in those very rare cases where the phenomena 
agree but in one point; so that although truth is acquired, 
yet it is so vague and indefinite as to be oftentimes prac- 



OF LOGIC AS PRACTICALLY APPLIED. 137 

tically worthless. In the example just given, all that we can 
be sure of is, that the power of conducting heat is in some 
manner connected with the possession of metallic attributes. 
If, therefore, we would arrive at a clearer notion of causes, 
we must seek for some method of singhng out the desired 
conditions from among the set which have been presented to 
us by the canon of agreement. 

Now, as an effect necessarily follows from its cause, except 
where there is a counteracting cause (which would be a new 
condition), we may conclude, that when, of two cases, one 
contains the phenomenon under investigation, and the other 
does not, the cause is not to be sought among the conditions 
common to both. If, therefore, we observe a case which 
does not exhibit the phenomenon, but all of whose conditions 
are contained in the set pointed out by the canon of agree- 
ment, we shall be enabled to ehminate these conditions from 
the number among which the cause is to be found, and thus 
our limits of search will be much narrowed. A sufficient 
repetition of this process will eventually point out with defini- 
tion and certainty the law which we are endeavouring to 
discover; and thus it may be seen that in this we possess a 
method of complete efficacy, in all cases susceptible of its 
application. The canon which regulates the operation, and 
which is termed the canon of Difference, may be enunciated 
in the following manner : — 

2^. The cause will be found among the circumstances in 
which an instance, composed of a portion of the con- 
ditions set apart by the canon of agreement, but not 
containing the effect, differs from an instance which is 
composed of all such conditions. 
The example chosen for exhibiting the method of agree- 
ment is not adapted to illustrate that of difference, for we are 
unable to select any body which is totally destitute of conduc- 
tive powers as regards heat ; we must consequently make use 
of some other instance, and leave this to be dealt with here- 
after. Suppose we wished to discover the conditions upon 
which our hearing the sound of a bell depends : we should 
learn by the method of agreement that all bells, however they 
might differ in shape, size, tone, &c., yet, when sounding, 



138 OF LOGIC AS PRACTICALLY APPLIED. 

agreed in vibrating and in being placed in the atmosphere. 
Next, we should endeavour to obtain an instance of a bell 
being struck, and thus thrown into vibration, but under dif- 
ferent circumstances, which might result in the sound being 
no longer heard. This would be effected by striking the bell 
in the exhausted receiver of an air-pump, when we should be 
unable to hear any sound ; and the condition in which the 
instances differed, i.e., the presence of an atmosphere, would 
consequently be the cause of sound being audible. 

We have just seen, however, that the method of difference 
is always inapplicable when no instance of the phenomenon's . 
non-occurrence can be obtained ; a circumstance which would 
be a great hindrance towards the acquirement of truth, w^ere 
we unable to find any remedy. But this is not impossible, 
for although the canon of difference is much more powerful 
than that of agreement, yet it is similarly restricted, as, by its 
means, we can only discover absolute laws, without any 
reference to quantity. Accordingly, w^e mtist now endeavour 
to obtain some knowledge of the means whereby the latter 
object may be accomplished. 

Among the uniformities of invariable sequence which 
come within our observation, we cannot fail to remark the 
existence in most cases of a certain ratio between cause and 
effect ; between antecedent and consequent. Thus, a small 
dose of arsenic produces no visible effect upon a man's con- 
stitution ; a larger dose makes him ill ; and a still greater 
quantity kills him ; w^hile beyond this limit no extension of 
its deadly effect can occur. Or, in blasting rocks, the work 
done is altogether dependent upon the weight .of gunpowder 
used ; assuming, of course, that the modus operandi remains the 
same. We are, consequently, led to the conclusion that the 
effect is always directly proportional to the cause, and that a 
variation in one is attendant on, or followed by, a correspond- 
ing variation in the other. But in one of the examples men- 
tioned above, this law does not appear at first sight to be 
universally true, for w^e have said that however large the 
quantity of arsenic may be, it can do no more than produce 
death ; and this leads us to the consideration that, for prac- 
tical purposes, apparent limits are often assigned to the law 



OF LOGIC AS PRACTICALLY APPLIED. 139 

in question, a cause being still regarded as the same with 
reference to the effect, although some condition has disap- 
peared. In the case alluded to, it is evident that the com- 
plete antecedent of death is composed of the poison capable 
of acting upon some organism, together with the organism 
itself in a state of life ; but it is equally evident that when 
death has supervened, the conditions existing are such as not 
to be capable of producing a similar effect, for the object to 
be destroyed no longer exists. The law is, therefore, seen to 
be universal, when we adopt the strict signification of *' cause" 
as formerly explained ; but at present we may safely assign 
those limits which are rendered necessary by our immediate 
apprehension of *' invariable sequence.'* 

The canon then of Proportional Variation runs thus : — 

3°. Whenever a phenomenon varies proportionately to the 
variation of some condition, there exists a uniformity 
of necessary sequence between them. 

The employment of this doctrine will enable us to arrive 
at truths which would otherwise be inaccessible. Take, for 
instance, the determination of the properties which cause 
metals to conduct heat. We find that no two possess equal 
conductive powers, and, also, that no two possess similar mo- 
lecular constitution ; in like manner we ascertain that any 
variation in the arrangement of the particles in a single metal 
occasions a corresponding variation of its conductive power ; 
but as our means of observation do not at present enable us 
to assign any distinct ratio between the variations of each 
separate mode of constitution, and the induced variations of 
conductivity, we can only conclude that some uniformity of 
dependence exists, without attempting to fix its precise law. 
I have purposely chosen an example of this extreme nature, 
as by it is shown that the canons of induction will at all 
times suffice to assure us of the right path to pursue, even in 
cases where the imperfect state of science precludes our 
attaining any immediate proximity to ultimate truth. 

We have now discussed the three principal canons of induc- 
tion ; there are, however, various practical corollaries and 
rules which spring from them, and as it would be impossible 
to consider each of these separately in a treatise like the 



140 OF LOGIC AS PRACTICALLY APPLIED. 

present, I think it best to proceed at once to the investi- 
gation of the other processes employed in the attainment of 
truth, and then to give an account of some scientific dis- 
coveries which will exhibit in a concrete form the develop- 
ment and application of such doctrines as we have examined. 

3°. Of Deduction^ Hypothesis, and Verification, By induc- 
tion we are enabled to arrive at general truths. When these 
are employed for the ascertainment of any particular truth 
not previously estabhshed we are said to deduce. Thus, 
induction has taught us that all beings which possess the attri- 
butes of humanity are mortal ; therefore, w^hen a fresh nation 
is discovered in Central Africa, we may with certainty predict 
that they are subject to death. Or, from the laws which have 
been found to regulate the respective motions of the bodies 
forming the solar system, astronomers can accurately foretell 
eclipses and other results of the changes that continually take 
place in the relative positions of the sun and its attendant 
planets. These judgments are the product of deduction based 
upon prior induction, and it is, therefore, commonly main- 
tained that the sole and ultimate foundation for all our know- 
ledge of truth is experience, i,e,, our observation of particular 
facts. This view, however, we have shown to be but par- 
tially correct, as the primary operation to which we traced 
the process of induction, consisted of a deduction from obser- 
vation referred to a general principle — of a syllogism, in fact, 
and, as such, amenable to the laws of mediate inference. Formal 
Logic, therefore, is the ultimate judge of all the mental ope- 
rations with w^hich thought is concerned ; and deduction is 
the first step made in our search after truth. Consequently, 
the title of the present division of Reflection must be held to 
refer to a secondary and derivative process of deduction, em- 
ployed for the purpose of utilising the laws determined by 
the original deductive operation which, on account of its 
strongly marked and distinguishing features, has received the 
name of Induction. 

In all scientific inquiries it is seldom found that single 
causes are in operation ; but as the inductive method is better 
adapted for the ascertainment of individual than of general 
laws, it usuallv makes us alone conversant with the relation 



OF LOGIC AS PRACTICALLY APPLIED. 141 

subsisting between solitary cases of antecedents and conse- 
quents. Here, then, we have the special province of deduc- 
tion pointed out, viz., the determining of the effects neces- 
sarily resulting from a combination of causes. And as this 
is done by a series of syllogistic reasonings, it will not require 
analysis in the present place, as we have alread}^ considered 
these at full length in the chapter upon syllogisms. I may, how- 
ever, remark that the finest examples of the deductive method 
will be found in the mathematical sciences, such as geometry 
and algebra, where the vast body of general truths are all 
derived from a proper union of a few simple laws. 

I have said that by induction we usually arrive at indivi- 
dual laws, i.e., at law^s which are appUcable to single or to 
few phenomena. By this I would be understood to mean, 
that the laws thus acquired will, in general, merely suffice to 
explain the sequence in the cases under direct consideration, 
or in cases essentially similar, being quite unserviceable when 
we attempt to extend their sphere. Thus, the phenomena of 
falling bodies led at first to the inference that it was the 
nature of most terrestrial matter to move dowm wards ; and a 
consideration of the planetary motions resulted in the con- 
clusion that orbits were circular, because of the perfection 
supposed to inhere in that species of curve. And even when 
more correct notions prevailed, laws were for long enter- 
tained, which assumed different sequences of causation as 
existing between celestial and terrestrial motions, it being 
reserved for Sir Isaac Newton to point out by a process of 
deduction, that the one law of gravitation was the regulating 
principle of the solar system, extending its influence from the 
determination of the cosmical cycles, to the least important of 
the movements taking place upon the earth's surface. 

It is not, however, always possible at the first blush to 
cbtain such laws by induction, as may suffice w^hen developed 
by the deductive method, for the full appreciation of the phe- 
nomena under investigation. In such cases the resort of the 
philosopher is hypothesis, which, when properly employed, 
vrill often suggest those observations that are capable of 
affording the grounds required by induction ; but as regards 
the formation of hypotheses, all rules are of little avail, for 



142 OF LOGIC AS PRACTICALLY APPLIED. 

success must entirely depend upon that natural sagacity, the 
possession of which is in a great measure the characteristic of 
genius. At the same time, it is quite possible to indicate the 
manner in which a hypothesis should be treated, and to point 
out the purposes it will best serve. 

A hypothesis, then, is the supposition of some law which shall 
serve to explain such sequences as have become the objects of 
observation. It is, therefore, employed when the cases in 
question are incapable of the particular collation required by 
the inductive canons, or their corollaries ; that is to say, when 
the facts cannot of themselves lead to any determined truth ; 
and when once the hypothesis has been framed it should be 
used deductively ; first, with a view to ascertain if the results 
thence arising correspond with the actual instances observed ; 
and in the next place, to infer the existence of new phenomena, 
which may then be sought for, and which, if discovered, will 
render probable the truth of the supposition. This duplicate 
process is termed verification, but, as just described, cannot 
be considered complete ; the hypothesis being spoken of, as 
thereby shown to be *' probably," not *^ certainly," true. In 
many cases, however, an extension of verification may 
amount to a perfect induction, for if we first prove that the 
supposed law is of such a nature as to account for the pheno- 
mena already observed, and to predict the occurrence of fresh 
examples; and, then, in addition, show that no other suppo- 
sition could offer a similar explanation, we shall satisfy the 
requirements of the canons of agreement and difi*erence, thus 
establishing the hypothesis as a true law. 

It will also be seen that in verification we have a most 
important adjunct of deduction, for when the latter process 
has, from the results of induction, arranged a system of laws, 
we may test the accuracy of these by employing them to 
explain observed phenomena, and to foretell facts that yet 
remain to be discovered ; and if in this manner we are led 
to satisfactory conclusions, we shall be enabled to strengthen 
the primary induction by means of the additional evidence 
thus obtained. Experiment is perhaps the most common 
method of verification, and deals exclusively with the pre- 
diction of sequences ; in fact, every operation of practical life 



OF LOGIC AS PRACTICALLY APPLIED. 143 

is an experiment by which we confirm afresh the laws de- 
duced by the various sciences. Our ships and buildings are 
all constructed in accordance with the principles of mechanics ; 
the art of agriculture is successful proportionately as it con- 
forms to chemical laws ; the safety of every sailor depends 
upon a special application of mathematics ; and thus we 
continually become more and more convinced of our ability 
to attain truth by means of a strict adherence to those 
mental laws which it is the office of Logic to discover and 
explain. 

4^. Of Analogy, The framing of any hypothesis is never 
a work of chance, i.e., a mere guess, in the strictest sense of 
the word, but is usually suggested by some circumstances of 
the observed phenomenon. Of these circumstances, the only 
one which it will be necessary to mention here, is analogy, 
which, it will be borne in mind, has already required our 
attention, when we were discussing the subject of fallacies. 
It was then described as the similarity of relations, and argu- 
ments both false and true were noticed as being founded 
thereupon. We must not, however, suppose that complete 
certainty may be attained by analogical reasoning ; as at the 
best, one can only infer a very strong degree of probability for 
the law deduced; this being treated hypothetically, i.e., as a 
provisional principle, until fully verified, when it of course 
assumes the position of an established truth. It will, there- 
fore, be obvious, that the cogency of any argument from 
analogy must depend altogether upon the special features of 
the case ; and, accordingly, I shall not attempt to give an 
exposition of the various analogical methods. The student 
may, however, gain a very good idea of analogy in general, 
by carefully considering the following resume of a celebrated 
problem, viz,, whether the planets are inhabited. 

In the first place, it is requisite that we should be put in 
possession of a certain number of facts, upon the basis of 
which we may found our argument. And, for reasons which 
will shortly appear, these facts should consist of similarities 
observed to exist between the earth and the other planets. 
Accordingly, a judicious use of the telescope has enabled us 
to accumulate the truths which follow. We find that Mercury, 



144 



OF LOGIC AS PRACTICALLY APPLIED. 



Venus, and Mars, are each provided with an atmosphere ; and 
so distinctly is this visible, that we can clearly perceive the 
morning and evening twilight on Venus ; we find, too, that 
clouds exist in these atmospheres, thus showing the existence 
of meteorological phenomena, such as rain, hail, snow, winds, 
&c., upon the respective planets. Again, it is ascertained 
that Mercury, Venus, and Mars revolve upon their axes, 
giving rise to the regular production of night and day, the 
respective lengths of these differing only by a few minutes 
from that which obtains upon the earth ; and, as the axis of 
Mars is inclined to the plane of his orbit at an angle very 
similar to the obliquity of the terrestrial ecliptic, it follows 
that as far as the sun is concerned, the seasons in both planets 
do not vary to any great extent, while very good reasons 
exist for supposing the same thing to occur in Mercury and 
Venus also. Nor does much variety obtain in the supply of 
light and heat to the four bodies of which we are speaking, 
whether reference be made to its uniformity or intensity ; 
and, as regards the effect of gravity, it is found that the 
weight of bodies upon the surface of Venus are very similar 
to those upon the earth, and that weights upon Mercury and 
Mars are about half as heavy. Lastly, the existence of con- 
tinents and seas has been observed upon Mars ; his polar 
regions being eternally covered with snow, the limits of 
which extend in winter and contract in summer. 

Having thus found that certain similarities exist between 
the earth and its neighbouring planet, we must, in the next 
place, ascertain what bearing these conditions have upon the 
phenomena of life. Nor does this require a lengthened 
investigation, for it will be immediately apparent, that on the 
earth all life is exactly adapted to, and depends upon, such 
physical circumstances as the existence of light, heat, air, 
water, night, day, the succession of the seasons, the surface 
configuration of land and sea, &c., &c. Now, in their relation 
to life such as ours, the physical conditions of Mercury, Venus, 
and Mars, may be considered as identical with those of the 
earth, and, accordingly, we form the following syllogism 
based upon analogy, or, in other words, upon a similarity of 
relations : — 



OF LOGIC AS PRACTICALLY APPLIED. 145 

Terrestrial phenomena are accompanied by life (A), 
Terrestrial phenomena are the phenomena of Mercury, 
Venus, and Mars (U) ; 

/. The phenomena of Mercury, Venus, and Mars, are ac- 
companied by life (A). 

If the premises are here granted, the argument is perfectly 
true, for A U A is a valid mood, and the proper method of 
refuting the syllogism would be to show the falsity of the 
minor premiss, which asserts, that as far as the present argu- 
ment is concerned, the physical phenomena of Mars, Venus, 
and Mercury are the same as those of the earth. 

With reference to Jupiter, Saturn, Uranus, and Neptune, 
the argument is of less force, as although they possess atmo- 
spheres, alternations of clay, night, and the seasons, together 
with water, &c., yet a consideration of their bulk, and other 
reflections, show that if life does exist upon them, it must 
differ considerably from terrestrial being : at the same time, 
it may be proved that there need be no greater variation 
between the life upon those planets and that upon the earth, 
than exists between the inhabitants of our torrid and frigid 
zones. Accordingly^, the analogical relation is much weaker, 
thus casting greater doubt upon the admissibility of the minor 
premiss. 

5°. Of Chance and Probabirdy. In the preceding remarks 
occasion has been taken to introduce the subject of proba- 
bihty ; and as" absolute certainty is of very rare occurrence in 
practice, it would not be advisable to close this notice of the 
reflective processes, without adding a few words upon the 
amount of belief which may be attached to certain judgments. 

This leads us to consider a certain restriction which attends 
the application of the canon of agreement. Its enunciation, 
it will be remembered, is as follows : — " A uniformity which 
is observed in two or more instances, may be considered as 
invariable and necessary ;" this referring to a law of causation 
existing between the common antecedent and consequent of 
the instances in question. Now it is evident that, for any- 
thing we can tell to the contrary, it may be necessary for the 
loliole of such antecedent to exist before the phenomenon can 
be produced ; and therefore, at the best, we can only generalise 

H 



14-6 OF LOGIC AS PRACTICALLY APPLIED. 

as to cases precisely similar in every respect to the observed 
instances. The law thus induced is termed an empirical law, 
and is of no use for the explanation of phenomena. But then 
again, it may happen that an effect is capable of being pro- 
duced by a variety of causes ; that is to say, that the common 
conditions of the instances may co-operate successively with 
the respective points of difference in giving rise to the same 
effect, assuming, of course, that we know of no connection 
between the various instances, all of them being equally inde- 
pendent. In such a case the effect would be termed the 
result of chance, as distinguished from law ; this meaning 
that we see no reason why the common conditions should be 
joined to any particular antecedent, or why, if so joined, the 
phenomenon should occur. 

It, therefore, becomes a matter of some interest to discover 
under what circumstances we are entitled to infer a causal 
instead of a casual uniformity, when the canon of agreement 
is alone used, and when, consequently, we are ignorant of 
any relation subsisting between the instances except such as 
are by this means discovered. These circumstances are 
usually determined in the following manner : — 

Suppose a series of instances among which we know none 
of the causes in operation, nor any necessary connection what- 
ever ; as for instance, the case of a box containing balls similar 
in every respect but colour, these being (Jrawn out separately 
by a person blindfolded. The question comes as to what 
probability there. is for any one colour to be drawn rather than 
another. Now the supposition being, that any one ball is 
.as; likely to be drawn as any other, it follows that if there 
were only two, black and white, the chances would be equal ; 
and so, in like manner, would it be if there were two of each 
colour, or three, or four, or, in fact, any number. But sup- 
pose there were two white to one black, then it is evident 
that of all the drawings possible, two would be in favour of 
white, and only one in favour of black, so that the " chances '* 
are two to one against black ; and in general it will be found 
that, as far as mere casualty is concerned, the probabiHty of any 
event occurring may be measured by the proportion of the 
number of cases in favour of such event to the total number 



OF LOGIC AS PRACTICALLY APPLIED. 147 

possible ; thus, in the first of our examples the probability of 
white was one -half, or one out of two ; in the second it was 
two-thirds, or two out of three. 

By similar investigations mathematicians have determined 
that the chance against any particular casual event recurring a 
given number of times in succession, is as the number of pos- 
sible events raised to a corresponding power to unity. Thus, 
four to one are the odds that heads will not be thrown twice 
in succession when a coin is tossed ; nine to one that heads 
will not occur three times successively, and so on. Also it 
has been shown that the chance of an event already observed 
again occurring may be represented by a fraction whose 
numerator is composed of the instances observed, increased 
by one, and whose denominator is the same number increased 
by two ; the chance against recurrence being that fraction, 
which, together with the chance for, would amount to unity. 
If, for example, I knew nothing of astronomy, and were to 
observe a comet appear for six successive nights in a certain 
portion of the sky, I might reasonably conclude that the 
chances for the phenomenon being again apparent on the 
next night were as seven -eighths to one -eighth, i.e,, as seven 
to one. 

Thus it will be seen that every increase in the number of 
times of observing the uniformity under similar conditions 
lends a vast amount of additional weight to the belief that 
there is some law concerned, and that the phenomenon is not 
a product of chance ; accordingly, it is considered generally 
requisite that before an empirical law can be laid down as 
such there must have been a sufficient number of instances 
observed to have eliminated chance ; that is to say, the uni- 
formity must have occurred a greater number of times than 
can be accounted for by the operation of chance. 

The importance of these considerations will be at once 
evident, when we reflect that the law of causation and all 
axiomatic principles are the products of the canon of agree- 
ment alone, and are, so far, but empirical laws. As, however, 
their limits of space and time comprehend all that we, as 
human beings, are concerned with, we may act upon them 
with a perfect assurance of their certitude. 

H 2 



148 OF LOGIC AS PRACTICALLY APPLIED. 

6°. Examples of Reflection, a. Tlie Discovery of Neptune, 
I shall take for my first concrete illustration of the reflective 
process that most stupendous achievement of modern astro- 
nomy, the discovery of the planet Neptune, which, present- 
ing as it does one of the completest triumphs of the human 
intellect, is pre-eminently calculated to display the vast acces- 
sion of power which original sagacity acquires by the proper 
development of the reasoning faculties. 

The process of verification first led to the above-mentioned 
discovery, and in the following manner. The Newtonian 
law of gravity, together with the laws of motion, had been 
found sufficient for the explanation and prediction of plane- 
tary movements until, in 1781, Uranus was discovered by 
Bir W. Herschel. This afforded a fresh test of those laws, 
and astronomers were not slow in availing themselves of the 
opportunity ; for not only did they compute tables, and con- 
struct ephemerides by which the future places of Uranus 
might be predicted, but they also calculated the positions which 
it had occupied in past times, and so were enabled to identify 
it with a supposed fixed star that had previously been observed 
at various periods by Flamsteed, Bradley, Mayer, and Lemon - 
nier. At the same time, however, it was found that the 
planet had not occupied the exact positions which were 
deduced from the above-mentioned laws, as its observed 
places deviated sensibly from the calculated ones ; it, therefore, 
became a matter of importance to ascertain the cause of such 
deviations ; and for this there were two hypotheses open — 
either the deviations were caused by chance, such as errors 
of observation, or by the operation of some definite and 
regular law. Accordingly, it was not until about 1840 that a 
sufficient number of observations had been accumulated so as 
to eliminate chance, and then the facts stood as follows. The 
planet was known to move in obedience to three causes — the 
laws of motion, the attraction of the sun, and the perturbations 
induced by the proximity of Jupiter and Saturn ; but a de- 
duction from these failed to explain the whole of Neptune's 
movements, for from 1795 to 1822 the observed places con- 
tinued, year by year to be in advance of those calculated, 
while from 1822 to 1830-1 a regression took place until the 



OF LOGIC AS PRACTICALLY APPLIED. 149 

tabular and observed positions agreed ; and tbis regression 
uniformly continued in tbe years succeeding 1830-1, so tbat 
tbe hypothesis of some regular disturbing cause was the 
only one tenable, chance being eliminated, and the planetary 
deviations being too small to cast any doubt upon the validity 
of the gravitativc and dynamical laws. At this point it was 
that Messrs. Le Verrier and Adams took up the question 
simultaneonslV, each, strangely enough, being in complete 
ignorance of the other's investigations ; and their first resort 
was to analogy ; for, knowing that the irregularities in the 
orbital movements of other planets were referable to the per- 
turbing effects of mutual attraction, they concluded that the 
same thing obtained with regard to Neptune ; that is to say, 
they inferred that all those disturbances which could not be 
accounted for by the influence of Jupiter and Saturn were 
caused by some planet hitherto unknown. But this was by 
no means sufficient, as mathematical considerations proved 
that any one of an infinite number of planets, varying in 
mass, distance, &c., would be capable of producing the devi- 
ations in question, so that the problem admitted of number- 
less solutions. It, therefore, became necessary still further 
to limit the question before any hope of arriving at a satis- 
factory answer could be entertained ; and this was done by a 
wider application of analogy. It was assumed that the un- 
known planet resembled those already discovered, in the 
plane of its orbit being nearly the same, in the direction of 
its motion being similar, in its orbit being an elHpse differing 
but little from a circle, and in its mean distance from the sun 
agreeing with Bode's law of progression. Also, as it was 
assumed to be a planet of the solar system, it w^as supposed to 
move in accordance with Kepler's laws, and from all these 
liypothetical conditions, the mass of the planet sought, together 
with the elements of its orbit, could be calculated very pre- 
cisely. This was accordingly done, and the results possessed 
a very high degree of probability, in consequence of the 
cogent analogical reasoning upon which they were based; so 
much so, indeed, that until something further could be ob- 
tained, the deduction might be assumed as true for all prac- 
tical purposes. But it wuU at once be evident that the ques- 



150 OF LOGIC AS PRACTICALLY APPLIED. 

tion was susceptible of a complete settlement, as it was only 
necessary to calculate the position which the supposed planet 
would occupy on any given night, and then to look for it in 
that place, when, if the hypothesis were correct, the planet 
would be immediately seen. Consequently, " on the 23rd of 
September, 1846, Dr. Galle, one of the astronomers of the 
Royal Observatory at Berlin, received a letter from M. Le 
Verrier, announcing to him that the longitude of the sought 
planet must then be 326^, and requesting him to look for it. 
Dr. Galle, assisted by Professor Encke, accordingly did ' look 
for it,' and found it that very night. It appeared as a star 
of the eighth magnitude, having the longitude of 326° 52', 
.and consequently only 52' from the place assigned by M. Le 
Verrier. The calculations of Mr. Adams, reduced to the 
same date, give for its apparent place 329° 19', being 2° 27' 
from the place where it was actually found." Thus the eh- 
mination of chance, combined with analogy, suggested a 
hypothesis, which assumed the rank of an estabhshed truth 
when the deductions from it received a complete verification. 
h, Kirchhoff's Researches on the Solar Spectrum, In this 
case the phenomenon observed was the occurrence of various 
dark lines in the spectrum of a sunbeam, and to discover the 
cause of these constituted the question at issue. The method 
of Difference was first employed by showing that solid or 
liquid bodies, when heated to incandescence, emit rays which 
produce spectra differing only from the solar spectrum in the 
absence of dark lines : the inference drawn from this fact 
being that the cause of such lines must be sought among the 
conditions in which the two cases differed. Now it was 
evident that both kinds of rays proceeded from incandescent 
bodies, and also passed through the terrestrial atmosphere, 
but the solar rays, in addition to this, had to pass through 
the sun's atmosphere, and, therefore, in this latter condition 
the sought cause should be found ; a conclusion which received 
additional strength from the analogical arguments of Sir David 
Brewster and Dr. Gladstone. In the next place, it had been 
found by experience that all transparent bodies emit, when 
incandescent, only those rays which they absorb when cold ; 
thus, red glass if strongly heated appears green, yellow glass 



OF LOGIC AS PRACTICALLY APPLIED. lol 

appears purple, &g. It was also known that the spectra of 
incandescent vapours consisted simply of bright lines upon a 
dark ground ; so, combining the two facts together, Kirch- 
hoff' conjectured that vapours comparatively cold would absorb 
the rays corresponding to such bright lines. Accordingly, 
he tried the experiment by causing the rays from a solid 
luminous body to pass through the vapour of sodium, and 
obtained a spectrum similar in every respect to that produced 
when no vapour was interposed, with the exception of two 
dark lines ; these were found to be identical in position with 
the two yellow lines composing the spectrum of luminous 
sodium vapour. But, on examining the solar spectrum, two 
dark lines were therein perceived which corresponded exactly 
with those resulting from the absorptive power of vapourised 
sodium, and, therefore, it was evident that the presence of 
such a body was one of the conditions of the solar atmo- 
sphere. In a similar manner it has been ascertained that iron, 
nickel, calcium, magnesium, barium, copper, &c., all sur- 
round the sun in a state of vapour, and thus produce those 
dark lines which formed the subject of investigation. The 
argument may be thus thrown into a train of syllogistic 
inference : — 

1. The facts observed being the production of uniform 
spectra by incandescent solids, and spectra with dark lines by 
the solar rays, we have the inductive syllogism, U U U : — 

The difference of conditions is the cause of the difference 
of phenomena. 

The solar atmosphere is the difference of conditions ; 
.*. The solar atmosphere causes the difference of the phe- 
nomena, viz., the dark lines. 

2. A deduction from a law previously established, AAA : — 
All transparent bodies when cold will absorb those rays 

which they emit when incandescent, 
Sodium vapour is a transparent body ; 
.*. Sodium vapour when cold absorbs those rays which it 
emits when luminous. 

3. This last conclusion is verified by experiment, and the 
facts now observed being the presence of two dark lines, both 
in the spectra from solar rays, and in those from incandescent 



152. OF LOGIC AS PRACTICALLY APPLIED. 

solids surrounded with sodium vapour, we construct a deduc- 
tive syllogism in A A I, Fig. 3, based upon the two former : — 
The cause of the two dark lines is sodium vapour, 
The cause of the two dark lines is the solar atmosphere ; 

.*. Some portion of the solar atmosphere is sodium vapour. 

I may mention that I have here purposely abstained from 
the consideration of more causes than one being capable of 
producing the same effect, as, otherwise, the argument would 
become too perplexed for my present intention, viz., to give 
an example of simple logical processes when practically 
applied. 

It would be easy to adduce many more instances of scien- 
tific discoveries, but the above, if thoroughly studied with a 
due recollection of the principles discussed in this treatise, 
will suffice to exhibit the method of analysing a complex 
argument into its logical elements ; and the student will be 
able to select for himself such other events in the history of 
philosophy as are well adapted for this purpose, thus putting 
his knowledge of mental laws to the test, and discovering what 
those particulars are which will be most advantageous for 
his individual pursuits. 

§ 4. Gondusion, 

Having now reached the end of our subject, it may not be 
amiss if we briefly consider the results which ought to flow 
from the study of a dissertation upon Logic. In the first 
place, we should be able to grasp the science as an organic 
whole, distinctly apprehending the nature of those inherent 
principles which compel the mind to think in one uniform 
manner, and forming a clear notion of the dependence which 
exists between them and our every act of acquiring know- 
ledge. Secondly, we should have become accustomed to 
concentrate our attention upon the process of thought, without 
any reference to the matters- about which it is employed. 
And, lastly, we should have learnt so to apply the practical 
principles which are deduced from a consideration of the 
primary mental laws, that without yielding to the blandish- 
ments of error, we may certainly attain the great temple of 
truth. 



OF LOGIC AS PRACTICALLY APPLIED. 153 

But I shall have written to very little purpose, if the reader 
be not in a position to recognise that great fact, the unity of 
philosophy, which, when once fully understood, lends a signi- 
ficance to all scientific truths, such as they otherwise would 
not possess ; for it is the office of Logic to show that every 
ramification of our knowledge, however diverse, may ulti- 
mately be traced back to one parent stem; and, so far from 
the various sciences differing as regards their nature, it be- 
comes a question as to whether the subjects concerning which 
they treat have any more than an apparent incompatibility. 
Therefore, he who would act in a truly philosophical spirit, 
must not remain satisfied with a crude, empirical acquaint- 
ance with isolated groups of facts, but should endeavour to 
obtain such general principles as may embrace them all; for 
then, not only would he obtain a more perfect knowledge of 
those facts themselves, but he would be enabled to gather 
many new truths, which, by any other method, must be lost 
for ever. And this may be observed in all the branches of 
learning : while the various facts are looked at in themselves, 
and by themselves, no great progress can be made ; but im- 
mediately that laws, even of a comparatively hmited nature, 
are discovered and borne in mind, then a vast impulse is 
given, the effects of which will speedily become apparent. 
At the same time, we should remember the intimate connec- 
tion of reflection with observation, and endeavour not to culti- 
vate one at the expense of the other. 

Logic, then, may be considered as abstract philosophy, 
that system of which all other sciences are but the concrete 
manifestations ; and, therefore, he alone can be justly termed 
a philosopher who has made himself acquainted with the 
laws that regulate the working of his own thoughts. But a 
mere acquaintance, in the ordinary sense of the word, will 
by no means suffice ; for, as Archbishop Thomson observes, 
" philosophy does not exist until the mind of the student 
begins to work for itself with the principles it receives histo- 
rically ; to decompose and to compose anew, to criticise the 
arguments employed, to essay at least to push the confines of 
truth farther into the wilds of error and ignorance, and to 
leave her a wider territory." In other words, we should not 

H 3 



154 OF LOGIC AS PRACTICALLY APPLIED. 

become accustomed to acquiesce as a matter of course in the 
assertions with which we meet, nor to imagine that the sub- 
ject is capable of no further development ; but, by actively 
applying the powers of our own minds to the elucidation of 
the question, we should endeavour to ascertain the precise 
amount of truth which inheres in the principles laid down, 
and to add something, however small, to the previously 
accumulated store of knowledge. 

The end, accordingly, at which all should' aim who desire 
the proper cultivation of their intellects, is rectification and 
progression — the correct adjustment of opinions already en- 
tertained, and the establishment of views more wide and lofty ; 
for, as this can only be done by a recourse to the latent powers 
of their own understandings, it will assuredly result both in 
a surprising accession of vigour to the individual mind, and 
in great benefits to the world at large, Nor can it be doubted 
that the practice of thought, when duly controlled by the 
regular operation of its formal laws, must highly conduce in 
the promotion of mental calmness and sobriety : no longer led 
astray by the influence of passion, or deceived by the repre- 
sentations of the senses, the well-ordered intellect, secure and 
undisturbed, reviews by the light of necessary truth those 
facts which come under its notice, and delivers judgment in 
strict accordance with the immutable laws of nature. 

In conclusion, I would remark that by far the noblest subject 
of human investigation is the human mind. The science of 
astronomy may give rise to emotions of awe and sublimity as 
we contemplate the vast infinitude of space, with its myriads 
of worlds and systems of worlds ; geology may astonish us 
with its record of the marvellous forms of life which have 
successively inhabited the earth ; the physical sciences may 
endue us with power so prodigious, as to become almost 
miraculous ; but yet, the fascination which attends every 
inquiry into the nature of our own being, must always cause 
the study of mental philosophy to take its place as the most 
mysterious and attractive object of all our speculations. 



APPENDIX. 



A. 

On Judgments. 

Iisr the body of this treatise, I have (p. 27) described judg- 
ment as ^* the act of determining by comparison, whether one 
idea is or is not included within another,'^ and have referred 
it to the motive faculty of classification. But as the subject is 
one of great importance, and has much influence upon a due 
appreciation of logical science, I deem it advisable to append 
some further observations which shall enable the student to 
form a completer notion of the import which attaches to pre- 
dication. 

]S"ow the most useful manner of inti'oducing such remarks 
will be to criticise the most important objections which have 
been made to the above views ; and for this pui^ose I shall 
select the following passage from Mr. Mill's *^ System of 
Logic,'' (vol. i. p. 104). ** This theory appears to me a signal 
example of a logical error very often committed in logic, that 
of varepoy Trporepov, or explaining a thing by something 
which presupposes it. When I say that snow is white, I 
may and ought to be thinking of snow as a class, because 
I am asserting a proposition as true of all snow : but I am 
certainly not thinking of white objects as a class ; I am 
thinking of no white object whatever except snow, but only 
of that, and of the sensation of white which it gives me. 
A\Tien, indeed, I have judged or assented to the propositions, 
that snow is white, and that several other things are also 
white, I gradually begin to think of white objects as a class, 
including snow and those other things. Eut this is a con- 
ception which followed, not preceded, those judgments, and 



156 APPEi^DIX. 

therefore cannot be given as an explanation of them. Instead 
of explaining the effect by the cause, this doctrine explains 
the cause by the effect, and is, I conceive, founded on a latent 
misconception of the nature of classification.'' 

In the expression '^ when I say that snow is white,'' Mr. 
Mill evidently alludes to the formation of such a judgment 
hefore the conception of a class of white objects, for he says 
shortly after, *^ This [white objects as a class] is a conception 
which followed " the establishment of similar propositions ; 
and as this is the ground upon which he charges the classifi- 
catory doctrine of judgment with error, his argument will be 
sufficiently refuted by showing that it is impossible to form 
the proposition '^ snow is white," before recognising white 
objects as a class. 

And first, let Mr. Mill himself be brought forward as a 
witness : he says (vol. i. p. 30), " When we say snow is white, 
milk is white, linen is white, we do not mean it to be under- 
stood, that snow, or linen, or milk, is a colour. We mean that 
they are things having the colour." Therefore the meaning of 
the proposition is, so far, that snow is a white object. It must 
next be shown that we cannot think oi '^ a white object,'^ 
by itself, but that we always think of *' some (or all) white 
objects," that is, of a class; and this may be done by a 
reference to the process of abstraction. Por, *as was seen at 
an early stage of our logical studies, it is necessary that such 
a process should be completed before we are able to possess 
any common notion or abstract term ; and, therefore, the idea 
^^ white" is the result of comparison, reflection, abstraction, 
generalisation, and denomination, the first four of these 
being simultaneous, a fact which will become evident upon 
pushing our analysis a little further. Thus, suppose we had 
never obtained the idea of *^ white," or of any other common 
notion, and that we met with the object *^snow:" the 
impression produced upon our senses would be a combination 
of such sensations as solidity, granular structure, absence of 
what is commonly termed colour, &c., but we should find 
it altogether impossible to separate this compound idea into 
its various parts; consequently, the only notion obtained 
would be an intuition, and we should be unable to form any 
other judgment than that ^^snow is snow." Immediately, 
however, that we met with any other intuition, say ^^milk," 
we should receive an immense acquisition to our Imowledge ; 
we should instinctively, as it were, compare them, and thus 



APPENDIX, 157 

perceive that although the two objects resembled each other 
in some respects, yet that they differed in others ; that, for 
example, in one object a solution of molecular continuity was 
easily observable, while in the other such a condition did not 
obtain ; that snow offered some resistance to a change of shape, 
while milk did not ; but also that the intuitions produced by 
both were partly indistinguishable. This fact would compel 
us to recognise that the idea {^' snow ") which we had previ- 
ously considered as simple, was in reality compound ; or, in 
other words, that it was capable of division : for we should 
have sensible evidence that a part of it could exist without 
the remainder. Accordingly, we should see that snow and 
milk were separate objects, but yet, as far as our minds were 
concerned, partially identical ; that is to say, we should 
recognise a class composed of two individuals. JSTow the whole 
of the preceding mental action would take place in equal 
progression, for with the commencement and advance of 
comparison, would commence and advance, pari passu, reflec- 
tion, abstraction, and generalisation. Eut after this was 
concluded as far as would suit our more immediate purpose, 
we should take some measure to prevent our forgetting its 
results, and this would be the imposition of an abstract temi, 
together with its correlative concrete. In the present case we 
should term that sensation in which both intuitions agreed, 
'' whiteness," and then we should form the proposition ^^ snow 
and milk are white objects;'' or, in more detail, we should 
say, *' snow is white, and milk is white." Therefore, it will 
be evident that no judgment (excluding such as are tautologous) 
can be formed without the conception of a class composed of 
at least two individuals ; although, in most cases, a general 
name cannot be imposed nntil after the comparison of many ' 
objects, and the recognition of a proportionately larger class. 
But it must here be borne in mind, that when once we have 
gone beyond the idea of unity, there is no definite limit 
which we can impose npon our powers of imagination ; and, 
accordingly, no sooner is a general notion conceived, than we 
regard the class as hypothetically infinite. This hint will, 
I hope, prove sufficient to prevent the opinion being enter- 
tained that classification is merely ^^an arrangement and 
grouping of definite and hiown individuals ; " and that the 
doctrine above stated implies the theory, ^'that when names 
were imposed, mankind took into consideration all the indi- 
vidual objects in the universe, distributed them into parcels 



158 APPENDIX. 

or lists, and gave to the objects of each list a common name, 
repeating this operation toties quotiesj until they had invented 
all the general names of which language consists.'' (Mill's 
'' Logic," vol, i. p. 105.) 

It has now, I apprehend, been irrefragably demonstrated 
that the classificatory doctrine of predication rests upon valid 
grounds, and that the objections considered above are un- 
tenable. Indeed, so simple and natural is the theory, that 
even Mr. Mill himself, when not engaged in actual combat 
therewith, implicitly affords his support to it, as witness the 
following passage : — '' A child learns the meaning of the words 
man or white, by hearing them applied to a variety of individual 
objects, and finding out, by a process of generalisation and 
analysis of which he is but imperfectly conscious, what those 
different objects have in common." (Yol. i. p. 39.) If 
this mean that an abstract notion and its concrete can- 
not be formed from the observation of a single object — 
and certainly neither from the passage itself, nor from the 
context can I suppose any other signification intended — then 
the whole question at issue is granted, since the idea of a 
class is merely the conception of two or more individuals 
resembling each other in certain respects.'^' 

I have already taken occasion to protest against Archbishop 
Thomson's exposition of judgment, but my remarks must not 
be held to refer to anything beyond the terminology employed, 
as it is possible that the doctrine so ambiguously put forth, 
may, in all essential points, be that of classification. Thus, 
speaking of the proposition ^^AU men are animals," Dr. 
Thomson says, ^^ We mean by our judgment, not that men 
and animals are just the same things, but that men are 
^contained in [sic] the wider class animals." (^'Outlines," 
p. 151.) 

And as regards my own statement (p. 28) that the copula 
of a proposition signifies ^^the identicality of the subject and 
predicate, such identicality being, however, limited by the 
form of the proposition," I must refer the reader for a more 
complete explication of its import, to the foregoing analysis 
of the manner in which common terms are formed. 

^ It may be proper to observe that in the above quotations many of 

the italics are my own. 



APPENDIX. 



159 



B. 

On the so-called Immediate Inteeences. 

These are such arguments as were discussed under the 
heads of opposition, conversion, and coincident junction ; 
and since a universal misconception appears to exist regarding 
their real nature, it may be worth while to present the reader 
with some additional information upon this point. 

And first, it will be necessary to prove that an inference 
takes place in these processes, for many logicians exclude 
them altogether from the sphere of reasoning. ]N"ow, I can- 
not do this better than by adopting the words of Archbishop 
Thomson, a philosopher to whom the science of Logic is under 
very great obligations ; and therefore, without further apology, 
I proceed to quote the following remarks : — 

'^ Some logicians refuse the name of inference to this and 
similar processes [those named above], on the ground that 
' there is in the conclusion no new truth, nothing but what 
was already asserted in the premises, and obvious to whoever 
apprehends them.' That the conclusion is virtually asserted 
in the premises, is true not only of these immediate inferences 
but of all syllogisms whatever; even in the inductive, the 
mere consequence — the act of concluding — brings in nothing 
which is not known potentially as soon as we have the whole 
grounds before us. So that the objection proves too much; as 
it would disqualify a set of inferences which no one thinks of 
rejecting. If, however, there is absolutely nothing new — if 
the concession of the premiss is not only a virtual, but an 
actual and express declaration of the conclusion, there is no 
inference, but mere repetition. Eut who can say that * no 
unjust rulers are good ' is a bare repetition of ' all good rulers 
are just ? ' In the one we affirm, in the other deny ; in the 
one the subject of thought is * good rulers,' in the other, 
' unjust rulers.' They are, in these two points at least, dis- 
tinct judgments, and as the passing of the one makes it pos- 
sible, without further observation or decision upon facts, to 
collect the other, there is an inference. In many such cases, 
it is true, the inference is so obvious, so certain to occur upon 
the first glance at the premiss, that it seems needless to draw 
it out ; but all the inferences we are about to specify are used 
from time to time, and this entitles them to our consideration." 



160 APPENDIX. 

The above passage will suffice for tlie establishment of the 
arguments in question as inferences ; it now remains to prove 
that they are mediate inferences. And here it may be re- 
marked as somewhat singular, that so acute a thinker as 
Dr. Thomson should have made such a near approach to the 
whole truth, and yet should have grasped but a portion ; for 
it will be observed that although he clearly perceives the con- 
clusion to result from a process of reasoning, he still maintains 
that it is dependent upon one premiss only ; a doctrine which 
probably arises from the very fact that arrests his attention, 
viz., the obviousness and transparency of the inference — this 
rendering him loth to suppose tha existence of a syllogistic 
deduction in so simple an operation, as, in like manner, it 
prevented the older logicians from admitting the presence of 
any reasoning whatever, no matter how supposedly direct it 
might be. 

I shall, accordingly, proceed to enunciate the several princi- 
ples upon which the validity of the inferred propositions rests ; 
and if they are obviously essential, the doctrine here advo- 
cated must be admitted as established. 

1. Opposition: — 

a. Contradictory. Any two classes must he either mutually 
and wholly exclusive or mutually and partially i7iclusive. This 
canon is necessitated by the laws which regulate our thoughts, 
and therefore, as far as Logic is concerned, must be considered 
fundamental. Its meaning is that we cannot think of any 
two classes, except in one of the manners stated ; and from 
it are developed these judgments : — ^' If E be true, I is false ; " 
'af E be false, I is true ; '' " If I be true, E is false ; '' and 
^^ If I be false, E is true ; '^ which respectively serve as 
major propositions in any particular case where this kind of 
opposition may be employed, the judgment operated upon 
serving as a minor. Thus, admitting the fact that ^^no men 
have wings,'' we must also admit that the statement '*some 
men have wings " is false ; for, 

If E be true, I is false, 
E (^^ no men have wings ") is true ; 
.•. I (*^ some men have wings ") is false. 
!N"ow, a moment's inspection will show that unless the major 
be here assumed, there can be no inference. 

h. Contrary. Neither the mutual and total exclusion of two 
classes, nor their mutual and partial inclusion, can he thought 
at the same time with their mutual and total inclusion, By 



APPENDIX. IGl 

development from this canon we obtain sneh majors as may 
be required, varying with the form of the original proposi- 
tion ; for example, if the position of A be employed as a 
minor premiss we may conclude that E, TJ, 0, and Y are 
false, by employing the major '^If A be true, then E, TJ, 0, 
and Y are all false." 

c. Subaltern. Whatever relation exists letween tico classes, 
the same exists between any portions of those classes. Here 
will be observed a modification of Aristotle^s dictum; for 
when we assert that the whole of one class is or is not con- 
tained in another, we must also be able to assert that a 
portion of it is similarly characterised ; and so on, to a full 
exposition of the canon, with its resulting majors. 

d. Subcontrary. Any two classes must he either mutually 
and wholly exclusive {when, by the last canon, we may assert 
them as mutually and partially exclusive), or they must he 
mutually and partially inclusive. This canon is at once seen 
to be a corollary from the first and third ; it can only refer to 
cases of I and 0, the majors being respectively, ^^ If I be 
false, is true ; " and *^ If be false, I is true." 

2. Conversion : — 

a. Simple. Those magnitudes which coincide are equal. 
This canon, common both to geometry and logic, will hardly 
be questioned. The explication of its present import is that 
when two classes, or parts of classes, comprise the same 
objects, or when two individuals comprise the same ideas, 
they may at pleasure replace each other as subject and 
predicate in any form of proposition. AYe are, therefore, 
entitled to assume for majors, *^ If A be true, the correspond- 
ing Yis," etc. 

h. Privative. Every object of thought must he either a posi- 
tive idea or its correlate privative. Now, since these ideas are 
mutually and wholly exclusive, we are manifestly enabled to 
infer the presence of one from the absence of the other, and 
vice versa. Erom this development of the canon, we must 
educe such majors as may be required from time to time; 
thus — 

1^0 immaterialities are material. 
All forces are immaterialities ; 
.'. ITo force is material. 

3. Coincident Junction : — 

The canon of this doctrine is, ^^ Whatever is joined to one 
of two or more inseparable ideas, is joined to all.^^ That is to 



162 APPENDIX. 

say, if we must always think simultaneonsTy of two objects, 
and we think of one of these at the same time with a third, 
the other mnst in like manner be conceived. Accordingly, 
we may construct as many syllogisms as we please of the 
following form : — 

Whatever may be added to the subject of an admitted 
proposition may at the same time be added to its pre- 
dicate, 
" Eed '' may be added to the subject of the admitted pro- 
position, " metals are solids ; " 

.-.It may be added at the same time to the predicate — e.g., 
'' red metals are red solids." 

Thus have I shown that every so-called immediate inference 
is, in reality, of a syllogistic nature ; for let any of the above- 
mentioned majors be denied, and the conclusion is no longer 
valid. The object with which I set out is, therefore, attained ; 
but ere I conclude, it will be useful to make a few brief obser- 
vations upon some detached portions of the subject. 

I have then to remark that as regards simple conversion, it 
must not be thought of as only applicable to tautologous 
judgments ; for, as shown by the table given in page 45, every 
possible proposition may be simply converted. JN'or must it 
be held that the convertend and its converse are the expres- 
sions of the same operations of thought ; for confessedly, the 
respective subjects about which we think are different. There- 
fore, when, speaking of conversion. Sir William Hamilton states 
(^^ Logic," Appendix, Y. c.) that *^it is of no consequence, 
in a logical point of view, which of the notions collated " are 
'^ subject or predicate," he would appear either to have been 
bestowing too little attention upon the process of thinking, or 
to have expressed himself ambiguously. 

I may also mention that Mr. Mill, who repudiates the notion 
of inference when applied to the above processes, has himself 
made a remark which affords a key to the whole question. 
lie is alluding to ^^ such considerations as these, that contrary 
propositions may both be false, but cannot both be true ; that 
subcontrary propositions may both be true, but cannot both 
be false," etc., etc. ; which the reader will immediately recog- 
nise as modifications of the canons above given ; and says 
that ^'in this respect [«.^., as involving general principles], 
these axioms of Logic are on a level with those of mathematics." 
He also implicitly terms them *^ elementary generalisations," 
but yet does not see that any one operation of opposition, etc., 



AP^E^'D!X. 1G3 

is as regular a deduction from a '' general truth" as is any 
reasoning of geometry or algebra, which depends upon pre- 
cisely similar axioms. (Compare Mill's " Logic," Book ii. 
chap. 1, § 2.) 



c. 

On the Dictum de Omi^^i et !N'ijllo. 

This canon I have enunciated (p. 8) in the following terms : 
— ^^ AYhatever is affirmed or denied altogether of any whole, 
may in like manner be affirmed or denied of any individual 
part belonging to, or comprehended in that whole ; " and I 
have here used the word ^^ whole" (the customary term 
being *^ class") in order that the principle might be more 
obviously applicable to syllogisms having singular terms. It 
will, however, be necessary to present in this place a more 
explicit view of the dictum than I have hitherto done ; for 
otherwise, the objections frequently urged against that law 
might possibly be considered as unanswerable. 

AYe have seen already (article A) that the notion of a class, 
or a ** common notion," is the complex idea of an indefinite 
number of individual members all possessing the same cha- 
racteristic, and also that the notion of an individual, or a 
^' singular .notion," is the complex idea of an indefinite 
number of attributes, most of them being class-characteristics, 
and all possessing the same unity of connection. Therefore, 
as a *' class" and its '^members" are, for all present pur- 
poses, precisely equipollent with an ^ * individual " and its 
*^ attributes," I shall use the terms '^ whole" and ^^ parts," 
which will serve equally well to represent either of the 
former pairs. 

We are now able to perceive a fact which lies at the very 
root of the question, viz., that a ^^ whole" is not composed 
merely of its *^ parts," but that it contains in addition .the 
*' unity" which obtains among them. And also — as was 
shown in the sections of this treatise which discussed the 
subjects of formal induction, deduction, extension and com- 
prehension — we knovv^ that it is possible to direct at pleasure 
the major part of our attention upon either of the above con- 



164: APPENDIX. 

stituents of a '^ whole," upon the ''unity,'' or npon the 
''parts." 

Thus much premised, I have next to point out a very 
important distinction, viz., the relative powers of conceiving 
the "unity" and the "parts." The "unity" is obviously 
a single object of thought; the "parts" are, on the contrary, 
not merely a numerous, but an indefinitely numerous collection 
of such objects : therefore, while it is possible to form a clear 
and precise notion of the "unity," we can only obtain a 
vague and indefinite idea of the "parts." Hence it results 
that we can always direct a greater portion of our attention 
upon the " unity," than upon the " parts ; " for that which 
we can perform more easily, we can perform better ; and as 
a corollary, we see that the natural disposition of the mind 
is to regard the "unity" as pre-eminent, the "parts" as 
subordinate. 

The dictum results, from the facts thus proved : it asserts 
that whatever is recognised as belonging to, or excluded from, 
the " whole," when principally looked upon as the "unity," 
will be found to hold the same relation, not to the " parts " 
in a body — for they, although vaguely conceived, yet form an 
essential constituent of the " whole," and are at least co- 
extensive with "unity" — but to any one of the "parts," no 
matter whether it be already known as individually existing, or 
whether it have yet to be rescued from the depths of inde- 
finity. And as I have formerly shown that all judgments 
are classifications (Appendix A), and that all reasoning what- 
ever may be exhibited in syllogisms (^passim) — these doctrines, 
taken in connection with the proof just nowafi'orded, that the 
dictum is a necessary law of thought, will, I apprehend, make 
it evident that the Stagirite's canon is the organic principle of 
all inference. 

That the above remarks were not altogether uncalled for, 
I shall show by quoting the following passage from Mr. Mill's 
"Logic" (Eook ii. chap. ii. § 2); my reason for selecting 
this author being that he is one of the ablest and best known 
of the logicians adopting similar views : — 

' ' JN'ow, however, when it is known that a class, an universal, 
a genus or species, is not an entity per se, but neither more 
nor less than the individual substances themselves which are 
placed in the class, and that there is nothing real in the 
matter except those objects, a common name given to them, 
and common attributes indicated by the name ; what, I should 



APPENDIX. 16o 

be glad to know, do we learn by being told, that whatever can 
be affirmed of a class, may be affirmed of eveiy object contained 
in the class? The class is nothing but the objects contained 
in it ; and the dictum de omni merely amounts to the identical 
proposition, that whatever is true of certain objects, is true of 
each of those objects. If all ratiocination were no more than 
the application of this maxim to particular cases, the syllogism 
would indeed be what it has so often been declared to be, 
solemn trifling. The dictum de omni is on a par with another 
truth, which in its time was also reckoned of great importance, 
* Whatever is, is.' To give any real meaning to the dictum 
de omni, we must consider it not as an axiom, but as a defini- 
tion ; we must look upon it as intended to explain, in a cir- 
cuitous and paraphrastic manner, the meaning of the word 
class. "^^ The italics here are Mr. Mill's. 

In what points the above passage differs from the doctrine 
previously advocated, and which view is supported by the 
more weighty arguments, are questions that must be left for 
each reader to decide for himself. Suffice it if a clear state- 
ment of the facts involved has been put forward. 

I have frequently spoken of Aristotle's dictum as being the 
fundamental law of inference ; but I should here wish to 
qualify that expression by stating that I do not use the word 
*^ fundamental " in its most explicit sense; that is to say, I 
do not imply the non-existence of some more recondite and 
general principle. My only meaning is, that for all logical 
purposes, it will be sufficient to consider the dictum, i.e., the 
practical law by which the motive faculty of classification 
works, as the ultimate principle of thought as thought : to the 
end that we may not be compelled to encroach upon metaphysical 
ground. 

In this connection it may be useful to mention that by 
many writers the fundamental laws of thought have been 
given as follows : — 

1. The Law of Identity. ^^ A concept is equal to all its 
characters," or, **A thing is equal to itself." 

2. The Law of Contradiction. ^^ TThat is contradictory is 
unthinkable." 

3. The Law of Exclusion. ^' Either a given judgment must 
be true, or its contradictory ; there is no middle course." 

4. The Law of Sufficient Eeason. '' Whatever exists or is 
true, must have a sufficient reason why the thing or proposi- 
tion should be as it is, and not otherwise." 



IGG APPENDIX. 

I shall content myself with having called, the reader's 
attention to these laws, and shall not attempt to discuss them 
in the present place. I may, however, refer to Sir William 
Hamilton's fifth and sixth lectures upon Logic, as containing 
an able analysis of the principles in question. 



On the Syllogism consideeed as a Petitio Peincipu. 

The form which this objection to the syllogism generally 
assumes is thus stated by Mr. Mill : — 

'' It must be granted that in every syllogism, considered as 
an argument to prove the conclusion, there is a petitio principu. 
When we say, 

All men are mortal, 
Socrates is a man ; 

Therefore, 
Socrates is mortal ; 
it is unanswerably urged by the adversaries of the syllogistic 
theory, that the proposition, Socrates is mortal, is pre-supposed 
in the more general assumption, All men are mortal : that we 
cannot be assured of the mortality of all men, unless we are 
already certain of the mortality of every individual man : that 
if it be still doubtful whether Socrates, or any other individual 
you choose to name, be mortal or not, the same degree of 
uncertainty must hang over the assertion. All men are mortal : 
that the general principle, instead of being given as evidence 
of the particular case, cannot itself be taken for true without 
exception, until every shadow of doubt which could affect any 
case comprised with it, is dispelled by evidence aliunde, and 
then what remains for the syllogism to prove ? That, in 
short, no reasoning from generals to particulars can, as such, 
prove anything ; since from a general principle we cannot 
infer any particulars, but those which the principle itself 
assumes as known." 

** This doctrine," Mr. Mill goes on to add, '* appears to me 
irrefragable," and the mode of issuing from the difficulty 
which he adopts, is to deny that the syllogism as such is an 



m 0- ""^ 



APPENDIX. 167 

inference. He asserts that tlie same evidence wliicli enabled 
us to infer the general truth ^^AU men are mortal," would 
equally enable us to draw the particular conclusion ^^ Socrates 
is mortal; " and that a true representation of the reasoning 
process which takes place, would be to say that as Solon, 
Lycurgus, Pisistratus, and other individuals possessed the 
attribute mortality, and as Socrates resembles those indivi- 
duals in his possession of the attribute humanity, he will 
therefore resemble them in being mortal. This ^ ^ type of 
ratiocination," says Mr. Mill, **does not claim^ like the 
syllogism, to be conclusive from the mere fonn of expression ; 

nor can it possibly be so "Whether, from the attributes 

in which Socrates resembles those men who have heretofore 
died, it is allowable to infer that he resembles them also in 
being mortal, is a question of induction ; and is to be decided 
by the principles or canons which we shall hereafter recognise 
as tests of the correct performance of that great mental 
operation." 

It will thus be seen that in refusing the name of inference 
(strictly speaking) to syllogistic reasoning, and in referring it 
to induction, Mr. Mill evidently considers the latter as alto- 
gether different in nature from the syllogism. It would not 
be difficult to quote other passages to the same effect, thus — 
**This was induction, but bad induction; just as a vicious 
syllogism is reasoning, but bad reasoning," where the processes 
of induction and syllogism are contrasted. Consequently, the 
theory of induction maintained in the body of this treatise, is 
directly at variance with the views just stated ; for I have 
endeavoured to show that the inductive process is merely a 
peculiar species of deductive (syllogistic) inference, and 
depends altogether upon reasonings which assume the form of 
syllogisms. It is necessary, then, to produce some considera- 
tions which shall serve to establish the fact that Mr. Mill 
is mistaken in supposing induction to be independent of 
syllogism. 

IN'ow this point may, I think, be proved by using Mr. Mill's 
own words. First, as regards inductions in general, I find 
the following statement: — '^ It hence appears that if we 
throw the whole course of any inductive argument into a 
series of syllogisms, we shall amve, by more or fewer steps, 
at an ultimate syllogism, which will have for its major 
premiss the principle, or axiom, of the uniformity of the course 
of nature." A passage like this might apparently be held as 



168 APPENDIX. 

an admission of all that I require to prove ; I shall, however, 
push the matter a little further, and ask, Upon what does Mr. 
Mill rest his ^' ultimate major premiss ? '' The answer I find 
to be, ^^ We arrive at this universal law, by generalisation 
from many laws of inferior generality.'' Eut here another 
step presents itself, which leads us to inquire what it is that 
gives validity to this last-mentioned *^ generalisation," which 
is described in another place as being an ^* induction by 
simple enumeration — in other words, generalisation of an 
observed fact from the mere absence of any known instance to 
the contrary ; " or, to vary the expression, what makes us 
certain that the conclusion to which this generalisation 
conducts is true ? The only approach to a reply which Mr. 
Mill gives, is as follows : — 

*^The considerations which, as I apprehend, give, at the 
present day, to the proof of the law of uniformity of succession, 
as true of all phenomena without exception, this character of 
completeness and conclusiveness, are the following : — First, 
that we now know it directly to be true of far the greatest 
number of phenomena; that there are none of which we 
know it not to be true, the utmost that can be said being that 
of some we cannot positively from direct evidence affirm its 
truth ; while phenomenon after phenomenon, as they become 
better known to us, are constantly passing from the latter 
class into the former ; and in all cases in which that transition 
has not yet taken place, the absence of direct proof is accounted 
for by the rarity or obscurity of the phenomena, our deficient 
means of observing them, or the logical difficulties arising 
from the complication of the circumstances in which they 
occur ; insomuch that, notwithstanding as rigid a dependence 
on given conditions as exists in the case of any other pheno- 
menon, it was not likely that we should be better acquainted 
with those conditions than we are." 

Accordingly, the observed ground for the conclusion that 
all phenomena have a cause, is the fact that some have ; but 
there is no reason assigned for such an inference being valid. 
I can therefore only suppose that Mr. Mill implies the exist- 
ence of some mental law which assures us of a particular 
uniformity so characterised being sufficient to warrant the 
truth of the corresponding general uniformity. And this 
view is borne out by such statements as this — ^^ The un- 
prompted tendency of the mind is to generalise its experience 
provided this points all in one direction," which are to be 



APPENDIX. 169 

frequent!} met ^\'it]l in the work quoted, The result, thpji, at 
which we finally amve, is that the mind supplies a general 
law, according to which, if certain facts are ascertained by 
observation, a fixed conclusion must be obtained. Let us 
state this mental law, the observed facts, and the conclusion 
in the order named, thus : — 

A case of a certain particular uniformity is a case of the 

corresponding general uniformity, 
The case of some phenomena being caused is such a par- 
ticular uniformity ; 
.*. The case of some phenomena being caused is a case of 
all phenomena being caused. 

This evidently is nothing but a syllogism, and indeed is 
precisely the same syllogism as that to which, in the body of 
this treatise, I traced all induction. A comparison of the in- 
vestigation then followed out, with that just concluded, will 
thus show that Mr. Mill implicitly, and myself explicitly, are 
agreed in considering induction as but a species of syllogistic 
inference. 

It now remains to prove that the syllogism is not obnoxious 
to the charge of depending upon a petitio 2)rincipii ; and this 
may, I think, be done in two ways. First, making use of 
the fact recently established, that all reasoning whatever is 
syllogistic, it can fairly be maintained, that even if it were 
impossible to directly point out any flaw in the argument 
supporting the charge ; yet there must of necessity be one 
somewhere, or otherwise no valid inference could ever exist. 
But, secondly, the alleged fallacy may be disposed of, in the 
following manner, by a reference to the simple processes of 
thought. 

Taking the example already used, i. e., ^^All men are 
mortal, Socrates is a man ; therefore, Socrates is mortal," let 
us consider whether or not the major premiss alone contains 
the conclusion. The subject is the class ^' man " taken uni- 
versally, that is, as a whole, and accordingly, the object which 
occupies our thoughts is composed principally of the unity 
*' humanity." The predicate is the class *' mortal things," 
considered mainly with reference to a portion of its ** parts ; " 
and the import of the entire judgment is that ^' humanity " is 
one of the unities possessing '^ mortality," and that the parts 
which are connected together by humanity form a complex 
portion of the parts connected by mortality. Xow the only 
assertion which is here made respecting individual objects is 



170 



APPENB 



^.^aMJ-^'- 



that any case of '' humanity '^ is a case of ^' mortality/' and 
therefore it is 7iot implied that any intuitmi such as Socrates, 
Plato, or Junius, is mortal, until such intuition has been ana- 
lysed and found to contain *^ humanity." Then, indeed, I 
grant, the major premiss implies the conclusion ; hut then, it 
must be borne in mind, we are also in possession of the minor 
premiss, without which the conclusion would not he so implied. 
Accordingly, the major tells us that the general notion ^Vman " 
forms a portion of the general notion ^* mortal things ; " the 
minor, that the intuition Socrates forms a portion of the 
general notion **man;'' the conclusion, that the intuition 
Socrates forms a portion of the general notion '^mortal 
things.'' And thus it will also be seen, that both the major 
and minor premises separately contain the conclusion when 
both are admitted ; but that, unless this be the case, neither 
of them does. Therefore, as hoth premises are essential to 
the conclusion, there is no petitio principii. 

The above is necessarily but a mere outline of the argu- 
ment by which the syllogistic theory, as ordinarily, and I 
apprehend, justly received, may be defended. The full details 
cannot here be set forth, and therefore I must ask the reader 
to supply them himself, a task which will be easy when once 
he is in possession of the key to the whole question, viz., 
when he perceives the distinction which must be made 
between an intuition as an intuition, and an intuition resolved 
into its constituting general notions. 

In this article, the work quoted from is Mr. Mill's ^' Logic," 
and I annex a list of the passages referred to, in the order of 
their occurrence above. 

Book ii. chap. iii. § 2. 

Do. do. §7. 
Eook iii. chap. iv. § 3, note. 

Do. chap. iii. § 1. 

Do. chap. xxi. § 2. 

Do. do. §4. 

Do. chap. iii. § 2. 



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J:'^^ Six Legislative Enactments for the Guidance of Con- :l^i5 

;^c^ tractors, Merchants, and Tradesmen, i. An Act to 'f^'^i^ 

s^^l) f acilitato the remedies on Bills of Exchange and Promissory Notes, dr^ -^ 

^tA II. An Act to amend the Laws relating to Stamp Duties, and on i?,y 

:> ^X Bonds and Securities. III. The Newspaper Stamp Act, and the '^'/v 

L^ Transmission by Post of Periodicals, &c. lY. An Act to con- ^§^5 

solidate the Excise and Stamps and Taxes into one Board. V. An -{j^^A 

Act for facilitating arrangements between Debtors and Creditors. ^?i-) 

/!^M VI. An Act to amend the Law of Insolrency, Bankruptcy, and ^^ j 

-T/^* Execution. With an Index. Is. :>i'^ 

^ Sv/ords, &c., Memoir on. By CoL Mahet, translated by f^% 

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^j(t Modern Farming, Outlines of. By Robert Scott Bubx. ^^ 

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By Nathaniel White, Esq. 12mo., Is. %0^ 

Logic, Pure and Applied, a Treatise on. By S. H. Emmexs, r^^'' 

Esq. 12mo., Is. 6d. -K^^ 



?X^ Investing Money, Practical Hints for: with an Expla- y^- 
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^^ vi^ nation of the Mode of Transacting Business on the Stock Exchange. 



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_ By Franxis Playford, Sworn Broker. Third Edition, revised and C -, 

f(r± corrected. 12mo., Is. ^>^J 



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